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The POEM Monte Carlo electron transport computer code has been developed for the calculation of x-ray photoemission from surfaces and the calculation of x-ray transition zone dose near material interfaces. The x-ray photoemission calculation includes fore and back emission yields, energy spectrum, 1D and 2D angular distributions, 2D and 3D energy-angular distributions, and various moments of the distributions. The x-ray transition zone dose calculation includes 1D energy and charge deposition profiles and 1D energy and charge deposition profiles and 1D photo-Compton current and energy current profiles. The code has been optimized and Monte Carlo variance reduction techniques have been incorporated to minimize the run time requirements. The POEM code is described in detail. Applications of the code to x-ray photoemission and transition zone dose are discussed in detail; other applications are briefly discussed. A complete set of user instructions is included.