Explore the intricacies of Anti-de Sitter geometry and its applications to hyperbolic surfaces in this 46-minute lecture delivered by Andrea Seppi at the Erwin Schrödinger International Institute for Mathematics and Physics (ESI). Delve into advanced mathematical concepts as part of the Thematic Programme on "Geometry beyond Riemann: Curvature and Rigidity" held from September 11 to November 3, 2023. Gain insights into the complex relationships between Anti-de Sitter geometry and hyperbolic surfaces, expanding your understanding of non-Euclidean geometries and their implications in modern mathematics and physics.