This course is on the mathematical techniques of use in studying electron-based many particle problems: Physical examples are used at every available opportunity. Contents: An introduction to Solid-State Chemistry; An introduction to Band structures and Spaghetti; Second quantisation: The Hubbard model; Green\'s functions and the impurity problem: Peierls distortion; Hartree-Fock: Magnetism in the Hubbard model; The strong-coupling limit: Nagaoka\'s theorem; Classical and quantum spin physics; RKKY and the Kondo effect: Heavy fermions; Superconductivity: BCS theory; Two particle Green\'s functions: RPA and itinerant spin-waves. |