**[Cr:4, Lc:3, Tt:1, Lb:0]**

- Introduction and Motivation: Brief review of key concepts in quantum mechanics and
statistical mechanics.
- Phase Transitions: Concept of phase and phase diagrams, examples of phase
transitions, statistical mechanics and phase transitions, Landau theory of phase
transitions, order parameter, relation to statistical mechanics, Superconducting phase
transition.
- Theory of superconductors: Electrodynamics of superconductors, Ginzburg-Landau
theory, BCS theory, Abrikosovâ€™s theory of type II superconductors, Andersonâ€™s theory
of disordered superconductors, Unconventional supercondcutors, heavy Fermions,
Order parameter symmetry, Josephson effect and SQUID, Superconducting qubits.
- Topological phases of matter and topological phase transitions: Quantum Hall effect and the emergence of topological invariants, Topological band theory, Model Hamiltonians, Topological properties and protections, Characterizing topological materials, Topological states of quantum matter, Topological insulators, Topological crystalline insulators, Topological superconductors, Weyl and 3D Dirac semimetals, Topological phase transitions.

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