This course explores the theory and applications of linear and integer programming within network flow systems. Students will learn foundational concepts of network modeling and optimization, including minimum-cost flows, maximum flow and minimum cut problems, and shortest path algorithms. The course extends to advanced topics such as multicommodity flows, network design with fixed charges, and integer programming methods for routing, assignment, and complex network optimization. Through lectures and a hands-on project, learners develop the skills to formulate, analyze, and solve real-world network flow problems using cutting-edge optimization techniques.