Rasch models are an important staple of psychological research and find use in other subjects such as sociology and educational testing. This edited volume comprises twenty-one chapters written by leading experts who have closely cooperated to present a self contained and unified overview of results thus far scattered or waiting for journal publication. Together, the chapters survey the underlying theory of Rasch models and the associated statistical ideas, provide systematic access to the fundamental results and proofs, and present a variety of applications. A clear and current overview is given of the Rasch model for dichotomous and polychotomous responses per item, dealing with the fundamental assumptions, parameter estimation, fit tests, relations to other models, use of item banks, measurement of change and other fields of application.