This is an introduction to free probability, or rather to both classical and
free probability, which are twin sisters. We discuss in detail the foundations
and main results of both theories, by insisting on their common features, and
by using a light formalism, based on the moment method and standard calculus.
We include as well a discussion of more advanced aspects, in relation with
random matrices, groups and quantum groups, free geometry, operator algebras
and subfactor theory.

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