### 1. Basic theoretical concepts for quantum many body systems

Green functions and diagrammatic perturbation theory. Matsubara formalism.

Baym-Kadanoff-Luttinger-Ward functional. Scattering theory; Fermi liquid.

Schwinger-Keldysh perturbation theory; illustration on simple cases; introduction to quantum Boltzmann equation.

### 2. Quantum impurity models

Introduction to Anderson and Kondo models; 1d formulation.
Kondo model in quantum dots; Coulomb blockade.

Kondo temperature; local Fermi liquid; Abrikosov-Suhl resonance;
screening of the impurity; slave boson approximation; renormalization group approach; Non Crossing Approximation (NCA).

Generalized models; non-Fermi liquid fixed points.

Quantum impurity out of equilibrium. Introduction to multiple impurity models. Algorithms to solve quantum impurity models in and out of equilibrium : Monte-Carlo algorithms, Renormalization Group approaches.

An introduction to Dynamical Mean Field Theory.