Explore the fascinating world of Kerr black holes, binary systems, and gravitational waves in this comprehensive lecture by Nicolas Yunes from Montana State University. Delve into the history of pulsars and metrics, and gain a deep understanding of common coordinate systems and Killing tensors. Examine the concepts of Zero Angular Momentum Observers, static observers, and stationary observers. Learn about the intricate relationships between these phenomena and their significance in the field of astrophysics and gravitational physics. This lecture, part of the ICTP School on Geometry and Gravity, provides a solid foundation for understanding the complex nature of black holes and their interactions with surrounding space-time.