From the reviews: J. Neveu, 1962 in Zentralblatt fur Mathematik, 92.Band Heft 2, p. 343: Ce livre ecrit par l'un des plus eminents specialistes en la matiere, est un expose tres detaille de la theorie des processus de Markov definis sur un espace denombrable d'etats et homogenes dans le temps (chaines stationnaires de Markov). N.Jain, 2008 in Selected Works of Kai Lai Chung, edited by Farid AitSahlia (University of Florida, USA), Elton Hsu (Northwestern University, USA), & Ruth Williams (University of California-San Diego, USA), Chapter 1, p. 15: This monograph deals with countable state Markov chains in both discrete time (Part I) and continuous time (Part II). [...] Much of Kai Lai's fundamental work in the field is included in this monograph. Here, for the first time, Kai Lai gave a systematic exposition of the subject which includes classification of states, ratio ergodic theorems, and limit theorems for functionals of the chain.