  Large random matrices appear in different fields of mathematics and physics
such as combinatorics, probability theory, statistics, operator theory, number
theory, quantum field theory, string theory etc... In the last ten years, they
attracted lots of interests, in particular due to a serie of mathematical
breakthroughs allowing for instance a better understanding of local properties
of their spectrum, answering universality questions, connecting these issues
with growth processes etc. In this survey, we shall discuss the problem of the
large deviations of the empirical measure of Gaussian random matrices, and more
generally of the trace of words of independent Gaussian random matrices. We
shall describe how such issues are motivated either in physics/combinatorics by
the study of the so-called matrix models or in free probability by the
definition of a non-commutative entropy. We shall show how classical large
deviations techniques can be used in this context. These lecture notes are
supposed to be accessible to non probabilists and non free-probabilists.
