This book focuses on the mathematical formulation of astrophysical models for the light curves of eclipsing binary stars, and on the algorithms for evaluating and exploiting such models. This book will provide astronomers, both amateur and professional, with a guide for specifying an astrophysical model for a set of observations, selecting an algorithm to determine the parameters of the model, and estimating the errors of the parameters. It is written for readers with knowledge of basic calculus and linear algebra; appendices cover mathematical details on such matters as optimization, coordinate systems, and specific models.