**I)- Random matrices**

*Dyson's symmetry and Wishart's distributions*

*Orthogonal polynomials and the Riemann-Hilbert problem*

*The unitary ensembles, universality of correlations*

*The gaussians orthogonal and symplectic ensembles*

*Statistical estimators, applications: Nuclear Physics,
Quantum Chaos, the Riemann ζ-function*

**II)- Free probabilities**

*Free groups and random walks*

*Probability spaces and freeness*

*Tensor algebra and representation of free random variables*

*Additive and multiplicative free convolutions*

*Applications: free central limit theorem, free divisibility*

*Combinatorial aspects of free probabilities*

*Free entropy, free brownian motion, Fisher's information,
large deviations*

**III)- Supersymmetric methods**

*Grassmann variable and integrals*

*Gaussian integrals*

*Random matrices and SUSY*

*Random matrices and mesoscopic transport*

*The diffusive regime of Anderson's model*