The Rasch model for test analysis is described and compared with two-parameter and three-parameter latent-trait models. Conditional maximum likelihood equations for estimating item parameters are derived, and estimates of person parameters are described together with their confidence intervals. Goodness of fit tests are discussed, including a graphic test of item fit and two over-all tests. Characteristics of tests which may cause them not to fit the model are listed, together with strategies for developing tests. Applications of the Rasch model to optimizing test efficiency, test equating and linking, and to tailored testing are described. Some generalizations of the basic model and special cases are mentioned. PML, a FORTRAN IV computer program used in applying the Rasch model, is described in detail, and a number of bibliographical references are appended. (CTM)