The psychometric research done by G. Rasch between 1951 and 1959, which is explained and illustrated in this book, takes psychometrics from being purely descriptive to being a science of objective measurement. Individual centered statistics require models in which each individual is characterized separately and from which, given adequate data, individual parameters can be estimated. It is further essential that comparisons between individuals become independent of the particular instruments used within the same class. This work demonstrates possibilities for building models that meet these demands. Part A, Chapters 1 through 7, discusses the basic principles with as little reference to mathematics as is practical. Part B, Chapters 8 through 10, then gives a full account of the mathematical background of these models. The following chapters are presented: (1) "Introduction"; (2) "Oral Reading Tests. A Model for Misreadings"; (3) "Oral Reading Tests. A Model for Speed"; (4) "Shortcomings of the Models"; (5) "A Structural Model for Items of a Test"; (6) "Control of the Model"; (7) "Notions Implied in the Structural Model for Items"; (8) "Mathematics of the Model for Misreadings"; (9) "Mathematics of the Model for Reading Speed"; and (10) "Mathematics of the Model for Item Analysis." An appendix provides a note on the denotation of the tests mentioned. (Contains 29 tables, 44 figures, and 78 references.) (SLD)