Explore the intricacies of Anti-de Sitter geometry and its applications to hyperbolic surfaces in this 54-minute lecture delivered by Andrea Seppi. As part of the Thematic Programme on "Geometry beyond Riemann: Curvature and Rigidity" held at the Erwin Schrödinger International Institute for Mathematics and Physics (ESI), delve into advanced mathematical concepts that bridge the gap between theoretical geometry and practical applications. Gain insights into the fascinating world of non-Euclidean geometries and their relevance to modern physics and mathematics. This talk, which serves as a continuation of a previous lecture, offers a deeper understanding of the subject matter, making it ideal for graduate students, researchers, and professionals in the fields of mathematics, physics, and related disciplines.