Geometrical phases and adiabatic evolution. Berry phases, polarization. Chern number. Two level systems. Topological band theory. The Su-Schrieffer-Heeger model, boundary states. The integer quantum Hall effect. Chern insulators and the Haldane model. Two-dimensional topological insulators and the BHZ model. Topological insulators in three-dimensions. Topological semimetals. Transport in topological phases. 

Time permitting: Fractional quantum Hall effect, anyons. Topological superconductivity, Majorana fermions and non-Abelian statistics.