Landuer-Buttiker Method: quantum junctions, the Landauer formula, multi-channel scattering and transport, multi-terminal systems; Green Functions: Green functions and the scattering problem, matrix Green functions, advanced and retarded Green functions, Dyson equation, resonant transport; Quantum Tunneling: basics of quantum tunneling, tunneling Hamiltonian method, sequential tunneling; Electron-electron Interaction and Coulomb Blockade: electron-electron interaction in nanosystems, single electron box, single electron transistor, Coulomb blockade in quantum dots, cotunneling; Vibrons and Polarons: electron-vibron interaction in nanosystems, inelastic electron tunneling, local polaron, inelastic tunneling in single-particle approximation, sequential inelastic tunneling; Non-equilibrium Green’s Function: correlation and scattering functions, selfenergy and Green’s function, kinetic equation, calculation of self-energy, relation to Landauer-Buttiker formalism; Schwinger-Keldysh Formalism: non-equilibrium problem, ground-state formalism, closed time path formalism, non-equilibrium diagrammatics, the self-energy; Integer Quantum Hall Effect: classical Hall effect, quantum Hall effect, Landau levels, conductivity in filled Landau levels, robustness of the Hall effect, particles on a lattice; Fractional Quantum Hall Effect: Laughlin states, quasi-holes and quasi particles, anyons, composite fermions, half-filled Landau level; Topology and Berry Phase: adiabatic evolution and the geometry of Hilbert space, Berry phase and the Aharonov-Bohm effect, spin-1/2 Berry phase, Berry curvature of Bloch bands, anomalous velocity, topological quantization; Topological Matter: quantum hall fluid on a torus, hydrodynamic theory, superconductors as topological fluids, topological superconductors, edge states, bulk-edge correspondence, topological insulators, quantum anomalous Hall effect, Z2 topological invariants, topological insulators and interactions.