This volume, like its predecessor, Probability and Statistics by Example, Vol. 1, was initially conceived with the intention of giving Cambridge students an opportunity to check their level of preparation for Mathematical Tripos examinations. And, as with the first volume, in the course of the preparation, another goal became important: to give the general public a clearer picture of how probability- and statistics-related courses are taught in a place like the University of Cambridge, and what level of knowledge is achieved (or aimed for) by the end of these courses. In addition, the specific topic of this volume, Markov chains and their applications, has in recent years undergone a real surge. A number of remarkable theoretical results were obtained in this field which only twenty years or so ago was considered by many probabilists as a ‘dead’ zone. Even more surprisingly, an active part in this exciting development was played by applied research. Motivated by a dramatically increasing number of problems emerging in such diverse areas as computer science, biology and finance, applied people boldly invaded the territory traditionally reserved for the few hardened enthusiasts who until then had continued to improve old results by removing one or another condition in theorems which became increasingly difficult to read, let alone apply. We thus felt compelled to include some of these relatively recent ideas in our book, although the corresponding sections have little to do with current Cambridge courses.