Explore the first lecture on Aspects of Krylov Complexity delivered by Pawel Caputa as part of the "Quantum Information, Quantum Field Theory and Gravity" program at the International Centre for Theoretical Sciences. Delve into cutting-edge concepts at the intersection of quantum gravity, quantum information theory, and many-body physics. Gain insights into topics such as the AdS/CFT correspondence, emergent spacetime and gravity, quantum error correction, black hole information paradox, and information scrambling in chaotic quantum systems. Learn about the application of quantum information theory to quantum field theories and many-body dynamics, including entanglement structure and its role in characterizing phases of quantum matter. Discover how this multidisciplinary approach is advancing our understanding of fundamental physics and opening new avenues for research in quantum gravity and related fields.