Markov Chains and Stochastic Stability is one of those rare instances of a young book that has become a classic. In understanding why the community has come to regard the book as a classic, it should be noted that all the key ingredients are present. Firstly, the material that is covered is both interesting mathematically and central to a number of important applications domains. Secondly, the core mathematical content is nontrivial and had been in constant evolution over the years and decades prior to the first edition's publication; key papers were scattered across the literature and had been published in widely diverse journals. So, there was an obvious need for a thoughtful and well-organized book on the topic. Thirdly, and most important, the topic attracted two authors who were research experts in the area and endowed with remarkable skill in communicating complex ideas to specialists and applications-focused users alike, and who also exhibited superb taste in deciding which key ideas and approaches to emphasize.

When the first edition of the book was published in 1993, Markov chains already had a long tradition as mathematical models for stochastically evolving dynamical systems arising in the physical sciences, economics, and engineering, largely centered on discrete state space formulations. A great deal of theory had been developed related to Markov chain theory, both in discrete state space and general state space. However, the general state space theory had grown to include multiple (and somewhat divergent) mathematical strands, having much to do with the fact that there are several natural (but different) ways that one can choose to generalize the fundamental countable state concept of irreducibility to general state space.