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We report on the detection of Cepheids and the first distance measurement to the spiral galaxy NGC 1326-A, a member of the Fornax cluster of galaxies. We have employed data obtained with the Wide Field and Planetary Camera 2 on board the Hubble Space Telescope. Over a 49 day interval, a total of twelve V-band (F555W) and eight I-band (F814W) epochs of observation were obtained. Two photometric reduction packages, ALLFRAME and DoPHOT, have been employed to obtain photometry measures from the three Wide Field CCDs. Variability analysis yields a total of 17 Cepheids in common with both photometry datasets, with periods ranging between 10 and 50 days. Of these 14 Cepheids with high-quality lightcurves are used to fit the V and I period-luminosity relations and derive apparent distance moduli, assuming a Large Magellanic Cloud distance modulus (m-M) (LMC) = 18.50 +- 0.10 mag and color excess E(B-V) = 0.10 mag. Assuming A(V)/E(V-I) = 2.45, the DoPHOT data yield a true distance modulus to NGC 1326-A of (m-M)_0 = 31.36 +- 0.17 (random) +- 0.13 (systematic) mag, corresponding to a distance of 18.7 \pm 1.5 (random) \pm 1.2 (systematic) Mpc. The derived distance to NGC 1326-A is in good agreement with the distance derived previously to NGC 1365, another spiral galaxy member of the Fornax cluster. However the distances to both galaxies are significantly lower than to NGC 1425, a third Cepheid calibrator in the outer parts of the cluster.

We present an overview of the Carnegie-Chicago Hubble Program, an ongoing program to obtain a 3 per cent measurement of the Hubble constant using alternative methods to the traditional Cepheid distance scale. We aim to establish a completely independent route to the Hubble constant using RR Lyrae variables, the tip of the red giant branch (TRGB), and Type Ia supernovae (SNe Ia). This alternative distance ladder can be applied to galaxies of any Hubble Type, of any inclination, and, utilizing old stars in low density environments, is robust to the degenerate effects of metallicity and interstellar extinction. Given the relatively small number of SNe Ia host galaxies with independently measured distances, these properties provide a great systematic advantage in the measurement of the Hubble constant via the distance ladder. Initially, the accuracy of our value of the Hubble constant will be set by the five Galactic RR Lyrae calibrators with Hubble Space Telescope Fine-Guidance Sensor parallaxes. With Gaia, both the RR Lyrae zero point and TRGB method will be independently calibrated, the former with at least an order of magnitude more calibrators and the latter directly through parallax measurement of tip red giants. As the first end-to-end "distance ladder" completely independent of both Cepheid variables and the Large Magellanic Cloud, this path to the Hubble constant will allow for the high precision comparison at each rung of the traditional distance ladder that is necessary to understand tensions between this and other routes to the Hubble constant.

Distances of galaxies in the Hubble Space Telescope Key Project are based on the Cepheid period-luminosity relation. An alternative basis is the tip of the red giant branch. Using archival HST data, we calibrate the infrared Tully-Fisher relation using 14 galaxies with tip of the red giant branch measurements. Compared with the Key Project, a higher value of the Hubble Constant by 10% +/- 7% is inferred. Within the errors the two distance scales are therefore consistent. We describe the additional data required for a conclusive tip of the red giant branch measurement of H_0.

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The Cepheid period-luminosity relation is the primary distance indicator used in most determinations of the Hubble constant. The tip of the red giant branch (TRGB) is an alternative basis. Using the new ANU SkyMapper Telescope, we calibrate the Tully Fisher relation in the I band. We find that the TRGB and Cepheid distance scales are consistent.

Cepheid variables are used to derive a Virgo cluster distance of 16.0 +/- 1.5 Mpc. In conjunction with the Coma velocity and the well-established Coma/Virgo distance ratio, this yields a Hubble paprameter Ho = 81 +/- 8 km/s/Mpc. By combining this value with an age of the Universe of at least 16.8 +/- 2.1 Gyr, that is derived from the metal-poor globular cluster M92, one obtains f(Omega,Lambda) > 1.39 +/- 0.22. This value is only marginally consisitent with an Einstein-de Sitter universe with Omega=0 and Lambda=0, which has f=1. An Einstein-de Sitter universe with Omega=1 and Lambda=0, for which f=2/3, appears to be excluded at the 3-sigma level. It is shown that some small recent values of Ho resulted from the intrinsic dispersion in the linear diameters of galaxies, and from the fact that well-observed supernovae of Type Ia exhibit a luminosity range of ~20 at maximum light.

We report on the discovery of Cepheids in the Virgo spiral galaxy NGC 4535, based on observations made with the Wide Field and Planetary Camera 2 on board the Hubble Space Telescope. NGC 4535 is one of 18 galaxies observed as a part of The HST Key Project on the Extragalactic Distance Scale which aims to measure the Hubble constant to 10% accuracy. NGC 4535 was observed over 13 epochs using the F555W filter, and over 9 epochs using the F814W filter. The HST F555W and F814W data were transformed to the Johnson V and Kron-Cousins I magnitude systems, respectively. Photometry was performed using two independent programs, DoPHOT and DAOPHOT II/ALLFRAME. Period-luminosity relations in the V and I bands were constructed using 39 high-quality Cepheids present in our set of 50 variable candidates. We obtain a distance modulus of 31.02+/-0.26 mag, corresponding to a distance of 16.0+/-1.9 Mpc. Our distance estimate is based on values of mu = 18.50 +/- 0.10 mag and E(V-I) = 0.13 mag for the distance modulus and reddening of the LMC, respectively.

Cepheid-based distances to seven Type Ia supernovae (SNe)-host galaxies have been derived using the standard HST Key Project on the Extragalactic Distance Scale pipeline. For the first time, this allows for a transparent comparison of data accumulated as part of three different HST projects, the Key Project, the Sandage et al. Type Ia SNe program, and the Tanvir et al. Leo I Group study. Re-analyzing the Tanvir et al. galaxy and six Sandage et al. galaxies we find a mean (weighted) offset in true distance moduli of 0.12+/-0.07 mag -- i.e., 6% in linear distance -- in the sense of reducing the distance scale, or increasing H0. Adopting the reddening-corrected Hubble relations of Suntzeff et al. (1999), tied to a zero point based upon SNe~1990N, 1981B, 1998bu, 1989B, 1972E and 1960F and the photometric calibration of Hill et al. (1998), leads to a Hubble constant of H0=68+/-2(random)+/-5(systematic) km/s/Mpc. Adopting the Kennicutt et al. (1998) Cepheid period-luminosity-metallicity dependency decreases the inferred H0 by 4%. The H0 result from Type Ia SNe is now in good agreement, to within their respective uncertainties, with that from the Tully-Fisher and surface brightness fluctuation relations.

We report the detection of Cepheid variable stars in the barred spiral galaxy NGC 1365, located in the Fornax cluster, using the Hubble Space Telescope Wide Field and Planetary Camera 2. Twelve V (F555W) and four I (F814W) epochs of observation were obtained. The two photometry packages, ALLFRAME and DoPHOT, were separately used to obtain profile-fitting photometry of all the stars in the HST field. The search for Cepheid variable stars resulted in a sample of 52 variables, with periods between 14 and 60 days, in common with both datasets. ALLFRAME photometry and light curves of the Cepheids are presented. A subset of 34 Cepheids were selected on the basis of period, light curve shape, similar ALLFRAME and DoPHOT periods, color, and relative crowding, to fit the Cepheid period-luminosity relations in V and I for both ALLFRAME and DoPHOT. The measured distance modulus to NGC 1365 from the ALLFRAME photometry is 31.31 +/- 0.20 (random) +/- 0.18 (systematic) mag, corresponding to a distance of 18.3 +/- 1.7 (random) +/- 1.6 (systematic) Mpc. The reddening is measured to be E(V-I) = 0.16 +/- 0.08 mag. These values are in excellent agreement with those obtained using the DoPHOT photometry, namely a distance modulus of 31.26 +/- 0.10 mag, and a reddening of 0.15 +/- 0.10 mag (internal errors only).

This is an investigation of the period-luminosity relation of classical Cepheids in samples of different metallicity. It is based on 481 Cepheids in the Large and Small Magellanic Clouds from the blue and red filter CCD observations (most similar to V_J & R_J) of the French EROS microlensing project. The data-set is complete and provides an excellent basis for a differential analysis between LMC and SMC. In comparison to previous studies of effects on the PL-relation, the EROS data-set offers extremely well-sampled light curves and well-filled instability strips. This allows reliable separation of Cepheids pulsating in the fundamental and the first overtone mode and derivation of differential reddening. Our main result concerns the determination of distances to galaxies which are inferred by using the LMC as a base and using two color photometry to establish the amount of reddening. We find a zero-point offset between SMC and LMC which amounts to a difference between inferred and true distance modulus of 0.14 \pm 0.06 mag in the VI_c system. The offset is exactly the same in both sets of PL-relations - of the fundamental and of the first overtone mode Cepheids. No effect is seen on the slopes of the PL-relations, although the fundamental and the first overtone mode Cepheids have different PL slopes. We attribute the color and the zero-point offset to the difference in metallicity between the SMC and LMC Cepheids. A metallicity effect of that small magnitude still has important consequencies for the inferred Cepheid distances and the determination of H_0. When applied to recent estimates based on HST Cepheid observations, our metallicity dependence makes the low-H_0 values (Sandage et al. 1994) higher and the high-H_0 values (Freedman et al. 1994b) lower, thus bringing those

Using published photometry and spectroscopy, we construct the fundamental plane and D_n-Sigma relations in Leo I, Virgo and Fornax. The published Cepheid P-L relations to spirals in these clusters fixes the relation between angular size and metric distance for both the fundamental plane and D_n-Sigma relations. Using the locally calibrated fundamental plane, we infer distances to a sample of clusters with a mean redshift of cz \approx 6000 \kms, and derive a value of H_0=78+- 5+- 9 km/s/Mpc (random, systematic) for the local expansion rate. This value includes a correction for depth effects in the Cepheid distances to the nearby clusters, which decreased the deduced value of the expansion rate by 5% +- 5%. If one further adopts the metallicity correction to the Cepheid PL relation, as derived by the Key Project, the value of the Hubble constant would decrease by a further 6%+- 4%. These two sources of systematic error, when combined with a +- 6% error due to the uncertainty in the distance to the Large Magellanic Cloud, a +- 4% error due to uncertainties in the WFPC2 calibration, and several small sources of uncertainty in the fundamental plane analysis, combine to yield a total systematic uncertainty of +- 11%. We find that the values obtained using either the CMB, or a flow-field model, for the reference frame of the distant clusters, agree to within 1%. The Dn-Sigma relation also produces similar results, as expected from the correlated nature of the two scaling relations. A complete discussion of the sources of random and systematic error in this determination of the Hubble constant is also given, in order to facilitate comparison with the other secondary indicators being used by the Key Project.

In the last decade, over 7000 eclipsing binaries have been discovered in the Local Group through various variability surveys. Measuring fundamental parameters of these eclipsing binaries has become feasible with 8 meter class telescopes, making it possible to use eclipsing binaries as distance indicators. Distances with eclipsing binaries provide an independent method for calibrating the extragalactic distance scale and thus determining the Hubble constant. This method has been used for determining distances to eclipsing binaries in the Magellanic Clouds and the Andromeda Galaxy and most recently to a detached eclipsing binary in the Triangulum Galaxy by the DIRECT Project. The increasing number of eclipsing binaries found by microlensing and variability surveys also provide a rich database for advancing our understanding of star formation and evolution.

We present the analysis of multiband time-series data for a sample of 24 Cepheids in the field of the Large Magellanic Cloud cluster NGC1866. Very accurate BVI VLT photometry is combined with archival UBVI data, covering a large temporal window, to obtain precise mean magnitudes and periods with typical errors of 1-2% and of 1 ppm, respectively. These results represent the first accurate and homogeneous dataset for a substantial sample of Cepheid variables belonging to a cluster and hence sharing common distance, age and original chemical composition. Comparisons of the resulting multiband Period-Luminosity and Wesenheit relations to both empirical and theoretical results for the Large Magellanic Cloud are presented and discussed to derive the distance of the cluster and to constrain the mass-luminosity relation of the Cepheids. The adopted theoretical scenario is also tested by comparison with independent calibrations of the Cepheid Wesenheit zero point based on trigonometric parallaxes and Baade-Wesselink techniques. Our analysis suggests that a mild overshooting and/or a moderate mass loss can affect intermediate-mass stellar evolution in this cluster and gives a distance modulus of 18.50 +- 0.01 mag. The obtained V,I color-magnitude diagram is also analysed and compared with both synthetic models and theoretical isochrones for a range of ages and metallicities and for different efficiencies of core overshooting. As a result, we find that the age of NGC1866 is about 140 Myr, assuming Z = 0.008 and the mild efficiency of overshooting suggested by the comparison with the pulsation models.

We present the analysis of multiband time-series data for a sample of 24 Cepheids in the field of the Large Magellanic Cloud cluster NGC1866. Very accurate BVI VLT photometry is combined with archival UBVI data, covering a large temporal window, to obtain precise mean magnitudes and periods with typical errors of 1-2% and of 1 ppm, respectively. These results represent the first accurate and homogeneous dataset for a substantial sample of Cepheid variables belonging to a cluster and hence sharing common distance, age and original chemical composition. Comparisons of the resulting multiband Period-Luminosity and Wesenheit relations to both empirical and theoretical results for the Large Magellanic Cloud are presented and discussed to derive the distance of the cluster and to constrain the mass-luminosity relation of the Cepheids. The adopted theoretical scenario is also tested by comparison with independent calibrations of the Cepheid Wesenheit zero point based on trigonometric parallaxes and Baade-Wesselink techniques. Our analysis suggests that a mild overshooting and/or a moderate mass loss can affect intermediate-mass stellar evolution in this cluster and gives a distance modulus of 18.50 +- 0.01 mag. The obtained V,I color-magnitude diagram is also analysed and compared with both synthetic models and theoretical isochrones for a range of ages and metallicities and for different efficiencies of core overshooting. As a result, we find that the age of NGC1866 is about 140 Myr, assuming Z = 0.008 and the mild efficiency of overshooting suggested by the comparison with the pulsation models.

We explore the limits of photometric reductions of crowded stellar fields observed with the Wide Field and Planetary Camera 2 on board the Hubble Space Telescope. Two photometric procedures, based on the DoPHOT and DAOPHOT/ALLFRAME programs are tested, and the effects of crowding, complex sky background and cosmic-ray contamination are discussed using an extensive set of artificial star simulations. As a specific application of the results presented in this paper, we assess the magnitude of photometric biases on programs aimed at finding Cepheids and determining distances. We find that while the photometry in individual images can be biased too bright by up to 0.2 mag in the most crowded fields due to confusion noise, the effects on distance measurements based on Cepheid variables are insignificant, less than 0.02 mag (1% in distance) even in the most problematic cases. This result, which is at odds with claims recently surfaced in the literature, is due to the strict criteria applied in the selection of the variable stars, and the photometric cross checks made possible by the availability of multiple exposures in different filters which characterizes Cepheid observations.

The final efforts of the HST Key Project on the Extragalactic Distance Scale are presented. Four distance indicators, the Surface Brightness Fluctuation method, the Fundamental Plane for early-type galaxies, the Tully-Fisher relation and the Type Ia Supernovae, are calibrated using Cepheid distances to galaxies within 25 Mpc. The calibration is then applied to distant samples reaching cz~10000 km/s and (in the case of SNIa) beyond. By combining the constraints imposed on the Hubble constant by the four distance indicators, we obtain H0 = 71+/-6 km/s/Mpc.

We examine the suggestion that half of the HST Key Project- and Sandage/Saha-observed galaxies have had their distances systematically underestimated, by 0.1-0.3 mag in the distance modulus, due to the underappreciated influence of stellar profile blending on the WFC chips. The signature of such an effect would be a systematic trend in (i) the Type Ia supernovae corrected peak luminosity and (ii) the Tully-Fisher residuals, with increasing calibrator distance, and (iii) a differential offset between PC and WFC distance moduli, within the same galaxy. The absence of a trend would be expected if blending were negligible (as has been inherently assumed in the analyses of the aforementioned teams). We adopt a functional form for the predicted influence of blending that is consistent with the models of Mochejska et al. and Stanek & Udalski, and demonstrate that the expected correlation with distance predicted by these studies is not supported by the data. We conclude that the Cepheid-based extragalactic distance scale has not been severely compromised by the neglect of blending.

The distance to NGC 3319 has been determined from Cepheid variable stars as part of the Hubble Space Telescope Key Project on the Extragalactic Distance Scale. Thirteen and four epochs of observations, using filters F555W (V) and F814W (I) respectively, were made with the Wide Field Planetary Camera 2. Thirty-three Cepheid variables between periods of 8 and 47 days were discovered. Adopting a Large Magellanic Cloud distance modulus of 18.50 +- 0.10 mag and extinction of E(V-I)=0.13 mag, a true reddening-corrected distance modulus (based on an analysis employing the ALLFRAME software package) of 30.78 +- 0.14 (random) +- 0.10 (systematic) mag and the extinction of E(V-I) = 0.06 mag were determined for NGC 3319. This galaxy is the last galaxy observed for the HST H0 Key Project.

Significant progress has been made during the last 10 years toward resolving the debate over the expansion rate of the Universe. The current value of the Hubble parameter, Ho, is now arguably known with an accuracy of 10%, largely due to the tremendous increase in the number of galaxies in which Cepheid variable stars have been discovered. Increasingly accurate secondary distance indicators, many calibrated using Cepheids, now provide largely concordant measurements of Ho well out into the Hubble flow, and deviations from the smooth Hubble flow allow us to better measure the dynamical structure of the local Universe. The change in the Hubble parameter with redshift provided the first direct evidence for acceleration and "dark energy" in the Universe. Extragalactic distance measurements are central to determining the size, age, composition, and fate of the Universe. We discuss remaining systematic uncertainties, particularly related to the Cepheid calibration, and identify where improvements are likely to be made in the next few years.

The distance to NGC 7331 has been derived from Cepheid variables observed with HST/WFPC2, as part of the Extragalactic Distance Scale Key Project. Multi-epoch exposures in F555W (V) and F814W (I), with photometry derived independently from DoPHOT and DAOPHOT/ALLFRAME programs, were used to detect a total of 13 reliable Cepheids, with periods between 11 and 42 days. The relative distance moduli between NGC 7331 and the LMC, imply an extinction to NGC 7331 of A_V = 0.47+-0.15 mag, and an extinction-corrected distance modulus to NGC 7331 of 30.89+-0.14(random) mag, equivalent to a distance of 15.1 Mpc. There are additional systematic uncertainties in the distance modulus of +-0.12 mag due to the calibration of the Cepheid Period-Luminosity relation, and a systematic offset of +0.05+-0.04 mag if we applied the metallicity correction inferred from the M101 results of Kennicutt et al 1998.

The potential of gravitational lenses for providing direct, physical measurements of the Hubble constant, free from systematic errors associated with the traditional distance ladder, has long been recognized. However, it is only recently that there has been a convincing measurement of a time delay sufficiently accurate to carry out this program. By itself, an accurate time delay measurement does not produce an equivalently definite Hubble constant and the errors associated with models of the primary lens, propagation through the potential fluctuations produced by the large-scale structure and the global geometry of the universe must also be taken into account. The prospects for measuring several more time delays and the feasibility of making the corresponding estimates of the Hubble constant with total error smaller than ten percent are critically assessed.

Based on general relativity, it can be argued that deviations from a uniform Hubble flow should be thought of as variations in the Universe's expansion velocity field, rather than being thought of as peculiar velocities with respect to a uniformly expanding space. The aim of this paper is to use the observed motions of galaxies to map out variations in the Universe's expansion, and more importantly, to investigate whether real variations in the Hubble expansion are detectable given the observational uncertainties. All-sky maps of the observed variation in the expansion are produced using measurements obtained along specific lines-of-sight and smearing them across the sky using a Gaussian profile. A map is produced for the final results of the HST Extragalactic Distance Scale Key Project for the Hubble constant, a comparison map is produced from a set of essentially independent data, and Monte Carlo techniques are used to analyse the statistical significance of the variation in the maps. A statistically significant difference in expansion rate of 9 km/s/Mpc is found to occur across the sky. Comparing maps of the sky at different distances appears to indicate two distinct sets of extrema with even stronger statistically significant variations. Within our supercluster, variations tend to occur near the supergalactic plane, and beyond our supercluster, variations tend to occur away from the supergalactic plane. Comparison with bulk flow studies shows some concordance, yet also suggests the bulk flow studies may suffer confusion, failing to discern the influence of multiple perturbations.

A Cepheid-based calibration is derived for four distance indicators that utilize stars in the old stellar populations: the tip of the red giant branch (TRGB), the planetary nebula luminosity function (PNLF), the globular cluster luminosity function (GCLF) and the surface brightness fluctuation method (SBF). The calibration is largely based on the Cepheid distances to 18 spiral galaxies within cz =1500 km/s obtained as part of the HST Key Project on the Extragalactic Distance Scale, but relies also on Cepheid distances from separate HST and ground-based efforts. The newly derived calibration of the SBF method is applied to obtain distances to four Abell clusters in the velocity range between 3800 and 5000 km/s, observed by Lauer et al. (1998) using the HST/WFPC2. Combined with cluster velocities corrected for a cosmological flow model, these distances imply a value of the Hubble constant of H0 = 69 +/- 4 (random) +/- 6 (systematic) km/s/Mpc. This result assumes that the Cepheid PL relation is independent of the metallicity of the variable stars; adopting a metallicity correction as in Kennicutt et al. (1998), would produce a (5 +/- 3)% decrease in H0. Finally, the newly derived calibration allows us to investigate systematics in the Cepheid, PNLF, SBF, GCLF and TRGB distance scales.

Uncertainty in the metal abundance dependence of the Cepheid variable period- luminosity (PL) relation remains one of the outstanding sources of systematic error in the extragalactic distance scale and Hubble constant. To test for such a metallicity dependence, we have used the WFPC2 camera on the Hubble Space Telescope (HST) to observe Cepheids in two fields in the nearby spiral galaxy M101, which span a range in oxygen abundance of 0.7+-0.15 dex. A differential analysis of the PL relations in V and I in the two fields yields a marginally significant change in the inferred distance modulus on metal abundance, with d(m-M)/d[O/H] = -0.24+-0.16 mag/dex. The trend is in the theoretically predicted sense that metal-rich Cepheids appear brighter and closer than metal-poor stars. External comparisons of Cepheid distances with those derived from three other distance indicators, in particular the tip of the red giant branch method, further constrain the magnitude of any Z-dependence of the PL relation at V and I. The overall effects of any metallicity dependence on the distance scale derived with HST will be of the order of a few percent or less for most applications, though distances to individual galaxies at the extremes of the metal abundance range may be affected at the 10% level.

We propose a method of distance determination based on the internal structure and dynamics of disk galaxies. The method relies on the universal luminosity profile of a stellar disk represented by an exponential law. Calibrating nearby galaxies with known distances, it is found that the scale length of the disk is tightly correlated with the specific combination of central surface brightness {\it and} rotational velocity at a characteristic radius of 2.15 scale lengths from the center. This suggests that the scale length of the disk may be used as an indicator for extragalactic distance scale. The application of this relation to M51 and M100 allows us to arrive at the distances of about 6 Mpc and 14 Mpc, respectively, implying a Hubble constant of $H_0 = 92 \sim 94$ km s$^{-1}$ Mpc$^{-1}$.

We propose a method of distance determination based on the internal structure and dynamics of disk galaxies. The method relies on the universal luminosity profile of a stellar disk represented by an exponential law. Calibrating nearby galaxies with known distances, it is found that the scale length of the disk is tightly correlated with the specific combination of central surface brightness {\it and} rotational velocity at a characteristic radius of 2.15 scale lengths from the center. This suggests that the scale length of the disk may be used as an indicator for extragalactic distance scale. The application of this relation to M51 and M100 allows us to arrive at the distances of about 6 Mpc and 14 Mpc, respectively, implying a Hubble constant of $H_0 = 92 \sim 94$ km s$^{-1}$ Mpc$^{-1}$.

Since the launch of the Hubble Space Telescope nine years ago, Cepheid distances to 25 galaxies have been determined for the purpose of calibrating secondary distance indicators. A variety of these can now be calibrated, and the accompanying papers by Sakai, Kelson, Ferrarese, and Gibson employ the full set of 25 galaxies to consider the Tully-Fisher relation, the fundamental plane of elliptical galaxies, Type Ia supernovae, and surface brightness fluctuations. When calibrated with Cepheid distances, each of these methods yields a measurement of the Hubble constant and a corresponding measurement uncertainty. We combine these measurements in this paper, together with a model of the velocity field, to yield the best available estimate of the value of H_0 within the range of these secondary distance indicators and its uncertainty. The result is H_0 = 71 +/- 6 km/sec/Mpc. The largest contributor to the uncertainty of this 67% confidence level result is the distance of the Large Magellanic Cloud, which has been assumed to be 50 +/- 3 kpc.

Using the Hubble Space Telescope (HST) 37 long-period Cepheid variables have been discovered in the Fornax Cluster spiral galaxy NGC 1365. The resulting V and I period-luminosity relations yield a true distance modulus of 31.35 +/- 0.07 mag, which corresponds to a distance of 18.6 +/- 0.6 Mpc. This measurement provides several routes for estimating the Hubble Constant. (1) Assuming this distance for the Fornax Cluster as a whole yields a local Hubble Constant of 70 +/-18_{random} [+/-7]_{systematic} km/s/Mpc. (2) Nine Cepheid-based distances to groups of galaxies out to and including the Fornax and Virgo clusters yield Ho = 73 (+/-16)_r [+/-7]_s km/s/Mpc. (3) Recalibrating the I-band Tully-Fisher relation using NGC 1365 and six nearby spiral galaxies, and applying it to 15 galaxy clusters out to 100 Mpc gives Ho = 76 (+/-3)_r [+/-8]_s km/s/Mpc. (4) Using a broad-based set of differential cluster distance moduli ranging from Fornax to Abell 2147 gives Ho = 72 (+/-)_r [+/-6]_s km/s/Mpc. And finally, (5) Assuming the NGC 1365 distance for the two additional Type Ia supernovae in Fornax and adding them to the SnIa calibration (correcting for light curve shape) gives Ho = 67 (+/-6)_r [+/-7]_s km/s/Mpc out to a distance in excess of 500 Mpc. All five of these Ho determinations agree to within their statistical errors. The resulting estimate of the Hubble Constant combining all these determinations is Ho = 72 (+/-5)_r [+/-12]_s km/s/Mpc.

Using published HST Cepheid data from 25 galaxies, we have found a correlation between the P-L dispersion and host galaxy metallicity which is significant at the ~3sigma level in the V band. This result supports the suggestion that the metallicity dependence of the Cepheid P-L relation may be stronger than expected. The high observed dispersions in the HST Cepheid P-L relations have the further consequence that the bias due to incompleteness in the P-L relation at faint magnitudes is more significant than previously thought. In the HST sample, galaxies at higher distance tend to have higher metallicity. This means that when a full metallicity/incompleteness correction is made, a scale error in the published Cepheid distances is seen in the sense that the published distance moduli are increasingly underestimates at larger distances. This results in the average distance modulus to the four galaxies in the Virgo cluster core increasing from (m-M)_0=31.2+-0.19 to (m-M)_0=31.8+-0.17 with similar increases for the Fornax and Ursa Major clusters. For the 18 HST galaxies with good Tully-Fisher distances and (m-M)_0>29.5 the Cepheid-TF distance modulus average residual increases from 0.44+-0.09 mag to 0.82+-0.1mag indicating a significant scale error in TF distances and resulting in the previous Pierce & Tully TF estimate of H_0=85 reducing to H_0=58+-7. Finally, for the 8 HST galaxies with SNIa, the metallicity corrected Cepheid distances now imply a metallicity dependence of SNIa peak luminosity in the sense that metal-poor hosts have lower luminosity SNIa. Thus SNIa Hubble diagram estimates of both H_0 and q_0 may also require significant metallicity corrections.

We use the Expanding Photosphere Method to determine distances to 10 type II supernovae. The effects of asymmetries, extinction, and flux dilution are explored. Using empirical evidence and time-independent, spherical models which treat H and He in non-LTE, we show that blackbody corrections caused by flux dilution are small for type II supernovae in the infrared, and in the optical when their color temperatures are less than 6000~K. The extinction to a type II-P supernova can be estimated from its light curve: the uncertainty introduced into a distance measurement due to extinction is usually less than 10\%. Correcting for extinction and flux dilution we derive distances to 10 supernovae: SN 1968L, SN 1969L, SN 1970G, SN 1973R, SN 1979C, SN 1980K, SN 1987A, SN 1988A, SN 1990E, and SN 1990ae. The distance measurements span a wide range, 50 kpc to 120 Mpc, which is unique among the methods for establishing the extragalactic distance scale. The distances measured to SN 1970G in M101 and SN 1987A in the LMC are in good agreement with distances determined from Cepheid variable stars. Our distance to the Virgo Cluster, 22 +- 3 Mpc, is larger than recent distances estimates made using surface brightness fluctuations, planetary nebula luminosity functions, and the Tully-Fisher method. Using the distances determined from these type II supernovae we derive a value of $H_0 = 60 \pm 10$ km sec$^{-1}$Mpc$^{-1}$. This value is subject to errors caused by local deviations in the Hubble flow, but will soon be improved by applying the Expanding Photosphere Method to several distant type II supernovae.

The distance to NGC 4725 has been derived from Cepheid variables, as part of the Hubble Space Telescope Key Project on the Extragalactic Distance Scale. Thirteen F555W (V) and four F814W (I) epochs of cosmic-ray-split Wide Field and Planetary Camera 2 observations were obtained. Twenty Cepheids were discovered, with periods ranging from 12 to 49 days. Adopting a Large Magellanic Cloud distance modulus and extinction of 18.50+/-0.10 mag and E(V-I)=0.13 mag, respectively, a true reddening-corrected distance modulus (based on an analysis employing the ALLFRAME software package) of 30.50 +/- 0.16 (random) +/- 0.17 (systematic) mag was determined for NGC 4725. The corresponding of distance of 12.6 +/- 1.0 (random) +/- 1.0 (systematic) Mpc is in excellent agreement with that found with an independent analysis based upon the DoPHOT photometry package. With a foreground reddening of only E(V-I)=0.02, the inferred intrinsic reddening of this field in NGC 4725, E(V-I)=0.19, makes it one of the most highly-reddened, encountered by the HST Key Project, to date.

We report the detection of Cepheids and a new distance to the spiral galaxy NGC 2541, based on data obtained with the Wide Field and Planetary Camera 2 on board the Hubble Space Telescope (HST). A total of 25 exposures (divided into 13 epochs) are obtained using the F555W filter (transformed to Johnson V), and nine exposures (divided into five epochs) using the F814W filter (transformed to Cousins I). Photometric reduction of the data is performed using two independent packages, DoPHOT and DAOPHOT II/ALLFRAME, which give very good agreement in the measured magnitudes. A total of 34 bona fide Cepheids, with periods ranging from 12 to over 60 days, are identified based on both sets of photometry. By fitting V and I period-luminosity relations, apparent distance moduli are derived assuming a Large Magellanic Cloud distance modulus and mean color excess of 18.50 +/- 0.10 mag and E(B-V) = 0.10 mag respectively. Adopting A(V)/E(V-I)=2.45, we obtain a true distance modulus to NGC 2541 of 30.47 +/- 0.11 (random) +/- 0.12 (systematic) mag (D = 12.4 +/- 0.6 (random) +/- 0.7 (systematic) Mpc), and a total (Galactic plus internal) mean color excess E(B-V) = 0.08 +/- 0.05 (internal error) mag.

We report on the discovery of Cepheids in the field spiral galaxy NGC 3621, based on observations made with the Wide Field and Planetary Camera 2 on board the Hubble Space Telescope (HST). NGC 3621 is one of 18 galaxies observed as a part of The HST Key Project on the Extragalactic Distance Scale, which aims to measure the Hubble constant to 10% accuracy. Sixty-nine Cepheids with periods in the range 9--60 days were observed over 12 epochs using the F555W filter, and 4 epochs using the F814W filter. The HST F555W and F814W data were transformed to the Johnson V and Kron-Cousins I magnitude systems, respectively. Photometry was performed using two independent packages, DAOPHOT II/ALLFRAME and DoPHOT. Period-luminosity relations in the V and I bands were constructed using 36 fairly isolated Cepheids present in our set of 69 variables. Extinction-corrected distance moduli relative to the LMC of 10.63 +/- 0.07 mag and 10.56 +/- 0.10 mag were obtained using the ALLFRAME and DoPHOT data, respectively. True distance moduli of 29.13 +/- 0.18 mag and 29.06 +/- 0.18 mag, corresponding to distances of 6.3 Mpc and 6.1 Mpc, were obtained by assuming values of 18.50 +/- 0.10 mag for the distance modulus of the LMC and E(V-I) = 0.13 mag for the reddening of the LMC.

This paper presents the calibration of BVRIH$ Tully-Fisher relations based on Cepheid distances to 21 galaxies within 25 Mpc, and 23 clusters within 10,000 km/s. These relations have been applied to several distant cluster surveys in order to derive a value for the Hubble constant, H0, mainly concentrating on an I-band all-sky survey by Giovanelli and collaborators which consisted of total I magnitudes and 50% linewidth data for ~550 galaxies in 16 clusters. For comparison, we also derive the values of H0 using surveys in B-band and V-band by Bothun and collaborators, and in H-band by Aaronson and collaborators. Careful comparisons with various other databases from literature suggest that the H-band data, whose magnitudes are isophotal magnitudes extrapolated from aperture magnitudes rather than total magnitudes, are subject to systematic uncertainties. Taking a weighted average of the estimates of Hubble constants from four surveys, we obtain H0 = 71 +- 4 (random) +- 7 (systematic) km/s/Mpc. We have also investigated how various systematic uncertainties affect the value of H0 such as the internal extinction correction method used, Tully-Fisher slopes and shapes, a possible metallicity dependence of the Cepheid period-luminosity relation and cluster population incompleteness bias.