Markov Processes provides a bridge from an undergraduate probability course to a course in stochastic processes. The text is designed to be understandable to students who have taken an undergraduate probability course without needing an instructor to fill in any gaps. Clear, rigorous, and intuitive, the second edition builds on the successful first, used in courses and as a reference for those who want to see detailed proofs of the theorems of Markov processes. It contains copious computational examples that motivate and illustrate the theorems. This second edition presents a new chapter illustrating the utility of using digraphs to describe whether a Markov process is reducible, absorbing, etc. There are additional exercises, and some material has been applied in a number of fields, including economics, physics, and mathematical biology. This book begins with a review of basic probability, then covers the case of finite-state, discrete-time Markov processes. Building on this, the text deals with the discrete-time, infinite-state case and provides background for continuous Markov processes with exponential random variables and Poisson processes. It presents continuous Markov processes that include the basic content of Kolmogorov’s equations, infinitesimal generators, and explosions. This book concludes with coverage of both discrete and continuous reversible Markov chains. While Markov processes are touched on in probability courses, this book offers the opportunity to concentrate on the topic when additional study is required. It creates a more seamless transition to prepare the student for what comes next.