Explore the Hartree-Fock (HF) approximation in quantum mechanics through this 52-minute lecture presented by Volker Bach of TU Braunschweig at IPAM's Model Reduction in Quantum Mechanics Workshop. Delve into the accuracy of the HF approximation, Lieb's variational principle and its generalizations, generalized HF approximation, and symmetries and restricted HF approximation. Gain insights into the Hartree-Fock theory, energy minimizer, variation of principle, generalized one-particle density matrix, repulsion, symmetries, and relevant examples.