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