Many-body formalism: second quantization, Green function, perturbation theory, Feynman diagrams. BEC and superfluidity. Fermi liquids; Luttinger liquids, bosonization. Electron-phonon interactions and superconductivity. Quantum magnetism: exchange mechanisms; magnetic insulators, spin-wave theory; itinerant magnetism, spin-density waves. Magnetic impurities, Anderson model, Kondo effect.