This work is an in-depth study of the change point problem from a general point of view and a further examination of change point analysis of the most commonly used statistical models. Change point problems are encountered in such disciplines as economics, finance, medicine, psychology, signal processing, and geology, to mention only several. The exposition is clear and systematic, with a great deal of introductory material included. Different models are presented in each chapter, including gamma and exponential models, rarely examined thus far in the literature. Other models covered in detail are the multivariate normal, univariate normal, regression, and discrete models. Extensive examples throughout the text emphasize key concepts and different methodologies are used, namely the likelihood ratio criterion, and the Bayesian and information criterion approaches. A comprehensive bibliography and two indices complete the study.