Explore the intricacies of post-Newtonian expansion methods in this comprehensive lecture by Luc Blanchet from the Institut d'Astrophysique de Paris. Delve into advanced concepts and techniques used to approximate solutions in general relativity, gaining valuable insights into the mathematical framework employed to describe gravitational phenomena in weak-field, slow-motion regimes. Learn how these methods are applied to various astrophysical systems, including binary star systems and gravitational wave sources, and understand their significance in modern theoretical physics and astrophysics research.