Part I: Basics: Second quantization, Tight binding models of graphene, Dirac equation in 1D,2D and 3D, Existence of end (1D), edge (2D) and surface states (3D), Introduction of the topological regime in the Dirac equation.

Part II: Topological band theory: Concepts of geometric phase (Berry phase), the Chern number, Laughlin’s gauge argument, Hall conductance and the Chern number, Bulk-edge correspondence, Time reversal symmetry and the
Z-2 invariants Time-reversal invariant topological insulators, Kene-Mele model and Haldane models, Quantum spin Hall state, Applications to Topological electronic devices.

Part III: Advanced topics: The Bogoliubov-de Gennes formalism for superconductors, the Kitaev chain and topological superconductivity, Majorana Fermions and topological quantum computing, device realizations of Majorana braiding.