This book serves as a comprehensive guide to the fundamental principles and applications of probability, random variables, and stochastic processes. It thoroughly explores the mathematical frameworks and theories that underpin these topics, providing clear explanations and examples to elucidate complex concepts. The text is designed for advanced undergraduate and graduate students in engineering and the physical sciences, offering both theoretical insights and practical tools for solving real-world problems involving randomness and uncertainty. Through its detailed coverage, the book equips readers with the necessary skills to model and analyze random phenomena in various scientific and engineering contexts.