This course explores the principles and techniques of network optimization with a focus on applications in machine learning and data routing. Students will learn how to model networked systems using graph theory, apply linear and convex optimization methods, and implement algorithms for shortest paths, maximum flows, and spanning trees. The course also delves into advanced topics such as reinforcement learning for dynamic network optimization, graph neural networks (GNNs), and scalable distributed optimization for large-scale systems. By the end, learners will gain both theoretical insights and practical tools for designing efficient and intelligent networked systems.