Explore the intricacies of many-body quantum chaos in this comprehensive lecture by Douglas Stanford at the Institute for Advanced Study's Prospects in Theoretical Physics 2018 conference. Delve into topics ranging from classical chaos to thermal expectations, and examine the fundamental principles of quantum mechanics, including orthonormality and wave function properties. Investigate the differences between local and nonlocal systems, and gain insights into small perturbations in quantum systems. This in-depth talk provides a thorough exploration of the complex world of quantum chaos, offering valuable knowledge for physicists and researchers in the field.