The book "Markov Chains with Stationary Transition Probabilities" by Kai Lai Chung, published by Springer-Verlag in 1960, is a comprehensive treatise on the theory of Markov chains, focusing on chains with stationary transition probabilities. The author, a professor of mathematics at Syracuse University, presents the theory in two parts: one on discrete parameter and the other on continuous parameter Markov chains. The book aims to develop the theory independently, addressing questions that arise from the hypothesis of a denumerable state space. Key topics include the principal limit theorem, the strong Markov property, and the application of concepts like separability and measurability. The book also highlights the contributions of notable mathematicians such as A. A. Markov, Kolmogorov, Doeblin, Doob, and Paul Lévy. While the book assumes a basic understanding of probability theory, it is designed to be accessible to readers with a modern introductory course in probability. The author acknowledges the limitations of the book in covering specific applications and open problems, particularly in the area of nonrecurrent phenomena and the theory of boundaries.The book "Markov Chains with Stationary Transition Probabilities" by Kai Lai Chung, published by Springer-Verlag in 1960, is a comprehensive treatise on the theory of Markov chains, focusing on chains with stationary transition probabilities. The author, a professor of mathematics at Syracuse University, presents the theory in two parts: one on discrete parameter and the other on continuous parameter Markov chains. The book aims to develop the theory independently, addressing questions that arise from the hypothesis of a denumerable state space. Key topics include the principal limit theorem, the strong Markov property, and the application of concepts like separability and measurability. The book also highlights the contributions of notable mathematicians such as A. A. Markov, Kolmogorov, Doeblin, Doob, and Paul Lévy. While the book assumes a basic understanding of probability theory, it is designed to be accessible to readers with a modern introductory course in probability. The author acknowledges the limitations of the book in covering specific applications and open problems, particularly in the area of nonrecurrent phenomena and the theory of boundaries.