This book is a comprehensive introduction to discrete stochastic processes, designed to help students understand and apply these concepts in engineering, science, and operations research. The text focuses on building intuition about the structure of stochastic processes and their effects in real systems, rather than on specific applications. It uses simple examples to illustrate key concepts and emphasizes the importance of understanding both the application areas and the mathematical structure of stochastic processes. The book covers a wide range of topics, including Poisson processes, renewal processes, Markov chains, random walks, and martingales. It provides a thorough treatment of these topics, with an emphasis on clarity and understanding rather than computational ability. The text is written for engineering and operations research graduate students, many of whom have an engineering background. It requires more patience than typical engineering courses, as the goal is to develop a deep understanding of the subject. The book avoids the use of measure theory and presents mathematical ideas with minimal analysis. It is organized to provide a clear and logical progression of concepts, with a focus on clarity over formal rigor and simplicity over generality. The text includes numerous examples that show how results fail when conditions are not met, emphasizing the importance of understanding the underlying principles. The book is based on the author's experience in teaching and is intended to be a comprehensive resource for students and professionals in the field of stochastic processes. It is written in a clear and accessible style, with a focus on building a strong foundation in the subject. The text is supported by a variety of exercises and examples, which help students develop a deep understanding of the material. The book is a valuable resource for anyone interested in the application of stochastic processes in engineering, science, and operations research.This book is a comprehensive introduction to discrete stochastic processes, designed to help students understand and apply these concepts in engineering, science, and operations research. The text focuses on building intuition about the structure of stochastic processes and their effects in real systems, rather than on specific applications. It uses simple examples to illustrate key concepts and emphasizes the importance of understanding both the application areas and the mathematical structure of stochastic processes. The book covers a wide range of topics, including Poisson processes, renewal processes, Markov chains, random walks, and martingales. It provides a thorough treatment of these topics, with an emphasis on clarity and understanding rather than computational ability. The text is written for engineering and operations research graduate students, many of whom have an engineering background. It requires more patience than typical engineering courses, as the goal is to develop a deep understanding of the subject. The book avoids the use of measure theory and presents mathematical ideas with minimal analysis. It is organized to provide a clear and logical progression of concepts, with a focus on clarity over formal rigor and simplicity over generality. The text includes numerous examples that show how results fail when conditions are not met, emphasizing the importance of understanding the underlying principles. The book is based on the author's experience in teaching and is intended to be a comprehensive resource for students and professionals in the field of stochastic processes. It is written in a clear and accessible style, with a focus on building a strong foundation in the subject. The text is supported by a variety of exercises and examples, which help students develop a deep understanding of the material. The book is a valuable resource for anyone interested in the application of stochastic processes in engineering, science, and operations research.