  This is a book for absolute beginners. If you have heard about random matrix
theory, commonly denoted RMT, but you do not know what that is, then welcome!,
this is the place for you. Our aim is to provide a truly accessible
introductory account of RMT for physicists and mathematicians at the beginning
of their research career. We tried to write the sort of text we would have
loved to read when we were beginning Ph.D. students ourselves. Our book is
structured with light and short chapters, and the style is informal. The
calculations we found most instructive are spelt out in full. Particular
attention is paid to the numerical verification of most analytical results. Our
book covers standard material - classical ensembles, orthogonal polynomial
techniques, spectral densities and spacings - but also more advanced and modern
topics - replica approach and free probability - that are not normally included
in elementary accounts on RMT. This book is dedicated to the fond memory of
Oriol Bohigas.
