The distribution of a Gaussian random variable, moments and cumulants, multivariate moments and cumulants, Wick’s formula for the moments of a multivariate Gaussian random variable, genus expansion for the moments of the GUE, asymptotic freeness of independent GUE’s, free random variables.

Further topics include:

- free group factors, basic properties of freeness, and free cumulants.

- the R-transform and the S-transform.

- analytic methods, the Cauchy and Stieltjes transforms.

- compression of factors and fundamental groups of factors.

- free entropy.

- Haar unitaries, asymptotic freeness of random matrices, and the Weingarten function.

- operator-valued free probability

In addition to the book of Nica and Speicher mentioned above there are:

– P. Deift, Orthogonal polynomials and random matrices : a RiemannHilbert approach, Amer. Math. Soc., 2000,

– F. Hiai and D. Petz, The Semicircle Law, Free Random Variables and

Entropy, Amer. Math. Soc. 2000,

– M. Mehta, Random Matrices, 3rd ed., Elsevier, 2004,

– D. Voiculescu, K. Dykema, A. Nica, Free Random Variables, Amer.

Math. Soc. 1992.