Modern developments of Random Matrix Theory as well as pedagogical approaches to the standard
core of the discipline are surprisingly hard to find in a well-organized readable and
user-friendly fashion. This slim and agile book written in a pedagogical and hands-on style
without sacrificing formal rigor fills this gap. It brings Ph.D. students in Physics as well
as more senior practitioners through the standard tools and results on random matrices with
an eye on most recent developments that are not usually covered in introductory texts. The
focus is mainly on random matrices with real spectrum.The main guiding threads throughout the
book are the Gaussian Ensembles. In particular Wigner's semicircle law is derived multiple
times to illustrate several techniques (e.g. Coulomb gas approach replica theory).Most
chapters are accompanied by Matlab codes (stored in an online repository) to guide readers
through the numerical check of most analytical results.
