Mild introduction to free probability

Free probability theory was initiated around 1985 by Voiculescu in order to answer some questions concerning certain von Neumann algebras. Today is a self--standing mathematical theory with fascinating links to topics such as random matrices, asymptotic representation theory of symmetric groups, combinatorics, classical probability, operator algebras and many others. During the talk I would like to present a simple combinatorial introduction to the foundations of this theory and present very briefly some applications.