This book is concerned with Preisach type models of hysteresis. It is emphasized that these models are phenomenological in nature and, for this reason, they can be used for the mathematical description of hysteresis of various physical origin. Discussion in the book is by and large centered around the following topics: various generalizations and extensions of the classical Preisach model (with special emphasis on vector generalizations), finding of necessary and sufficient conditions for the representation of actual hysteresis nonlinearities by various Preisach types models, solution of identification problems for these models, numerical implementation and experimental testing of Preisach type models. Although the study of Preisach type models constitutes the main subject of the book, some effort is also made to establish some interesting connections between these models and such well known hysteresis models as: the critical state model for superconducting hysteresis, the classical Stoner-Wohlfarth model of vector magnetic hysteresis, thermal activation type model for viscosity.