This introduction to the theory of Markov chains describes a modern approach to determining the rate of convergence of a Markov chain to the stationary distribution as a function of the size and geometry of the state space. Part I focuses on techniques, with accessible examples. Part II covers more sophisticated techniques and presents several detailed case studies of particular families of chains. The authors develop tools for estimating convergence times, including coupling, strong stationary times, and spectral methods. Whenever possible, probabilistic methods are emphasized. The book includes many examples and provides brief introductions to some central models of statistical mechanics. Also provided are accounts of random walks on networks, including hitting and cover times, and analyses of several methods of shuffling cards. Chapter ending notes give references to original papers and provide suggestions for further reading. As a prerequisite, the authors assume a modest understanding of probability theory and linear algebra at an undergraduate level. Levin is affiliate with the University of Oregon. Annotation ©2009 Book News, Inc., Portland, OR (booknews.com)