Explore recent advancements in General Relativity through this 45-minute lecture by Gustav Holzegel and Peter Hintz, presented by the International Mathematical Union. Delve into Lorentzian manifolds, Einstein Equations, and the fundamental theorem of general relativity. Examine well-posed systems of PDEs, maximally symmetric solutions, and their stability. Investigate black hole solutions, perturbations, and toy stability models. Gain insights into non-linear stability proofs, the black hole interior, and developments in many-black-hole spacetimes. Enhance your understanding of cutting-edge research in this complex field of physics and mathematics.