An advanced course that focuses on the principles, models, and applications of Markov theory in analyzing and optimizing stochastic processes and systems. Markov theory provides a powerful framework for studying systems that undergo transitions between states based on probabilistic rules. This course introduces students to the theory, models, and techniques of Markov processes, equipping them with the skills to analyze, model, and optimize dynamic systems in various real-world contexts. Through a combination of theoretical concepts, practical examples, and hands-on exercises, students will develop proficiency in using Markov theory to analyze system behavior, predict outcomes, and make informed decisions to enhance efficiency and performance.