Wigner matrices and moments estimates.- Wigner’s theorem.- Wigner's matrices; more moments estimates.- Words in several independent Wigner matrices.- Wigner matrices and concentration inequalities.- Concentration inequalities and logarithmic Sobolev inequalities.- Generalizations.- Concentration inequalities for random matrices.

- Matrix models.- Maps and Gaussian calculus.- First-order expansion.- Second-order expansion for the free energy.- Eigenvalues of Gaussian Wigner matrices and large deviations.- Large deviations for the law of the spectral measure of Gaussian Wigner's matrices.- Large Deviations of the Maximum Eigenvalue.- Stochastic calculus.

- Stochastic analysis for random matrices.- Large deviation principle for the law of the spectral measure of shifted Wigner matrices.- Asymptotics of Harish-Chandra-Itzykson-Zuber integrals and of Schur polynomials.- Asymptotics of some matrix integrals.- Free probability.- Free probability setting.- Freeness.- Free entropy.

- Basics of matrices.- Basics of probability theory.