Explore a comprehensive lecture on quantum embedding theories presented by Dominika Zgid at IPAM's Advancing Quantum Mechanics with Mathematics and Statistics Tutorials. Delve into the physical and chemical motivations behind these theories, examining Green's function embedding and other approaches. Gain insights into the challenges of solving many-electron problems and learn about controlled, accurate approximations that are numerically tractable. Discover key concepts such as electronic behavior in solids, self-energy embedding theory, and the impurity problem. Understand the significance of hybridization and its role in quantum mechanics. Ideal for those interested in advanced quantum mechanics, computational chemistry, and materials science.