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The purpose of the book is to serve as a handbook for measurement specialists as well as to serve as a textbook for students in classes on the Bayesian approach to modern test theory. The book will also serve as a guide to the authors’ computer software implementations that will be made available via a website. This software supports the computation of the various models described in the book and can support readers in their own developmental work in IRT using advanced Bayesian techniques/models. The software implementations will be made available in the popular statistical packages Splus and R. The implemented new functions are built on Fortran code that is linked to the Splus and R environments. This approach leads to considerable reduction of computation time.