Explore the intricacies of comparable-mass binary systems in this lecture on black holes and gravitational waves. Delve into advanced topics such as post-Newtonian theory, relaxed Einstein equations, and the Dyer approach. Learn about Cartesian coordinates, the general procedure for analyzing binary systems, and the concepts of minimum distance and minimum radius. Examine the near zone and radiation zone in the context of gravitational wave emission. Gain insights from speaker Nicolas Yunes of Montana State University in this comprehensive presentation from the ICTP School on Geometry and Gravity.