Dedicated to the study of ergodicity and stability of stochastic processes this book provides a thorough and up-to-date investigation of these processes. The author is at the forefront of this growing area of research and presents novel results as well as established ideas. The term "stability" is used in this book to describe continuity properties of stationary distributions with respect to small perturbations of local characteristics. Comprising three parts, the first eloquently demonstrates the general theorems of ergodicity and stability for a comprehensive number of classes of Markov chains, stochastically recursive sequences and their generalizations. Expanding on the introduction, the second part considers ergodicity and stability of multi-dimensional Markov chains and Markov processes. For one-dimensional Markov chains special attention is paid to large deviation problems and transient phenomenon. Drawing upon the results presented throughout the book the final part considers their application in establishing conditions of ergodicity in communication and queueing networks. In particular, two types of polling systems are considered; Jackson networks and buffered random access systems related to the ALOHA algorithm. This text will have broad appeal to statisticians and applied researchers seeking new results in the theory of Markov models and their application.