1. Vector potential, gauge invariance, Aharanov Bohm, Dirac quantization eg = m hbar/2, sections instead of wave functions for the monopole.
2. Berry phase: origin, Berry potential, and flux, monopole at degeneracy , effect on dynamics.
3. Symmetries, unitary and anti, details of time reversal symmetry
4. Symmetries of lattice models and band theory
5. Su-Schreiffer-Heeger model : model, topology, various phases, edge states, continuum theory, charge fractionalization.
6. TKKN theory of Hall conductance as Chern number (from Kubo , with all details)
7. Chern bands, different expressions for Chern number , sigmaxy for Dirac sea
8. 1/2 Bernevig-Hughes-Zhang model : Dirac points, phases edges
10 IQHE as Topological insulator
11. TRI TI's Kane-Mele model, Z_2 classification, diagnosis of phases