From the reviews:

J. Neveu, 1962 in Zentralblatt fГјr Mathematik, 92.Band Heft 2, p. 343: "Ce livre Г©crit par l'un des plus Г©minents spГ©cialistes en la matiГЁre, est un exposГ© trГЁs dГ©taillГ© de la thГ©orie des processus de Markov dГ©finis sur un espace dГ©nombrable d'Г©tats et homogГЁnes 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."