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Data association and track association algorithms have been developed over the course of thirty years. Almost all technical papers that describe these association algorithms have begun the derivations by adopting log-likelihood ratios as the measure of association. At best, this starting point has obscured the assumptions necessary to use log-likelihood ratios. At worst, the log-likelihood ratios have been improperly defmed. This report provides the first known derivation of a track association algorithm from the first principles of Bayesian probability theory. By starting with first principles, all the assumptions that are necessary to derive an association algorithm are explicitly stated as the derivation proceeds. The correct form for the log-likelihood ratios is obtained later in the derivation and can be traced back to first principles. The pitfalls and deficiencies of poorly performing association algorithms are identified easily by comparing the algorithms with the full derivation. These deficiencies arise from such mistakes as the incorrect definition of the log-likelihood ratio, poor selection of the probability density functions, incorrect construction of the cost matrices, and the application of an algorithm to a system that violates the assumptions that were adopted during the algorithm construction. In addition, the firm grounding in Bayesian probability theory provides the means to easily extend the derivation to produce more complex association algorithms, such as feature-aided track association algorithms. The basic derivation provided in this report makes it clear that the ensemble of track association algorithms is much more extensive that most data fusion researchers would believe. These algorithms can be created by simply changing any of the derivation assumptions or the probability density functions.