Explore the theoretical connections between Anti-de Sitter/Conformal Field Theory (AdS-CFT) correspondence and celestial holography in this advanced physics lecture delivered by Massimo Taronna at the Galileo Galilei Institute. Delve into the fundamental principles of holographic duality and discover how insights from the well-established AdS-CFT framework can inform and guide the development of celestial holography, a promising approach to understanding quantum gravity in asymptotically flat spacetimes. Examine the mathematical structures, symmetries, and physical interpretations that bridge these two holographic paradigms, gaining valuable perspective on how lessons learned from AdS-CFT can illuminate the path toward a complete formulation of celestial holography and its applications to realistic gravitational systems.