Explore a comprehensive lecture on the ground-state energy of a Bose gas, delivered by Elliott H. Lieb at the Erwin Schrödinger International Institute for Mathematics and Physics (ESI). Begin with a quick review of the simple equation derived in 1963 for calculating the ground state energy E of a dilute Bose gas with 2-body repulsive interactions. Discover the famous LHY second order term for E and learn about recent findings showing remarkable agreement with Monte Carlo calculations in 3 dimensions for all densities. Uncover potentially unsuspected changes at intermediate density and gain insights into this fundamental topic in quantum physics. The 1-hour and 10-minute talk, held on March 7, 2023, offers a deep dive into the intricacies of Bose gas behavior and its mathematical description.