This book, "Discrete Stochastic Processes" by Robert G. Gallager, is part of the Kluwer International Series in Engineering and Computer Science, focusing on Communications and Information Theory. It aims to provide students with a deep understanding and intuition of stochastic processes, particularly in the context of engineering, science, and operations research. The author emphasizes the importance of building insight through simple examples and abstract concepts rather than complex calculations. The book covers various topics including Poisson processes, renewal processes, finite state Markov chains, Markov chains with countably infinite state spaces, Markov processes with countable state spaces, random walks, and martingales. Each chapter includes exercises and notes to enhance understanding. The text is designed for graduate students with an engineering background and is intended to develop a robust understanding of stochastic processes, rather than focusing on computational skills. The author draws inspiration from the theoretical and applied environment at MIT and acknowledges the contributions of numerous graduate students and colleagues who have helped refine the manuscript.This book, "Discrete Stochastic Processes" by Robert G. Gallager, is part of the Kluwer International Series in Engineering and Computer Science, focusing on Communications and Information Theory. It aims to provide students with a deep understanding and intuition of stochastic processes, particularly in the context of engineering, science, and operations research. The author emphasizes the importance of building insight through simple examples and abstract concepts rather than complex calculations. The book covers various topics including Poisson processes, renewal processes, finite state Markov chains, Markov chains with countably infinite state spaces, Markov processes with countable state spaces, random walks, and martingales. Each chapter includes exercises and notes to enhance understanding. The text is designed for graduate students with an engineering background and is intended to develop a robust understanding of stochastic processes, rather than focusing on computational skills. The author draws inspiration from the theoretical and applied environment at MIT and acknowledges the contributions of numerous graduate students and colleagues who have helped refine the manuscript.