This course provides an in-depth exploration of mathematical tools and applications essential for analyzing signals or data processing on graphs. Graphs are versatile representations used across various fields, including physical networks (like the Internet, sensor networks, smart grids, neural networks, social networks, and biological networks) and data structures (like image pixels or AI training datasets). This course blends theoretical foundations with practical applications, featuring hands-on exercises in graph signal processing (GSP). As a graduate-level course, it also delves into the latest research trends in GSP development. Students will develop a robust theoretical understanding necessary for network analysis and will address relevant security and/or privacy topics within advanced GSP technology.