Explore a comprehensive lecture on the nonlinear stability of the Schwarzschild metric without symmetry, delivered by Mihalis Dafermos from Princeton University at the Institute for Advanced Study. Delve into advanced topics in mathematical physics and analysis, including the Schwarzschild family, Kerr spacetime, and linear stability of Schwarzschild. Examine the main theorems, gauge invariant quantities, and the Einstein equations in double null gauge. Gain insights into the boundedness and decay for Teukolsky, wave equations on Kerr, and the proof of decay for Teukolsky on Schwarzschild. Investigate the transition from linear to nonlinear stability, reformulation of the linear stability theorem, and the challenges associated with nonlinear difficulties.