### 1. The replica and the cavity approaches to quenched disordered systems in mean field theory.

The Random Energy model, the computation of the free energy with the replica approach. Spin models; the computation of the free energy with both models (replica and cavity): their equivalence and relative advantages.

### 2. Complexity and all that (various kind of potentials).

Introduction of potential for constrained replicas and their computation in mean field theory.
Definition of complexity in mean field models and its possible extension to short range models.

### 3. The replica method for disordered systems without quenched disorder (e.g. structural glasses).

The dynamical transition for glasses. The MKK (Mari, Krzakala and Kurchan) and MK (Mari and Kurchan) models. Simulations of the models and analytic computations. More realistic models: the generalized MK model.

### 4. Corrections to mean field theory.

The loop expansion. Computations of the corrections in the case of a ferromagnet with a random magnetic field. Supersymmetry and dimensional reduction. Loop corrections to the replica potential.

### 5. Effective actions for glasses, renormalization group computations.

Identification of the leading infrared divergences. The computation of the effective action for glasses in various approximations. The Ginsburg criterion.

### 6. Slow dynamics.

The adiabatic approximation to slow dynamics; the replica approach; the emergence of mode-coupling like equations.