This
volume is based on lectures delivered at the 2013 AMS Short Course on
Random Matrices, held January 6-7, 2013 in San Diego, California.
Included
are surveys by leading researchers in the field, written in
introductory style, aiming to provide the reader a quick and intuitive
overview of this fascinating and rapidly developing topic. These
surveys contain many major recent developments, such as progress on
universality conjectures, connections between random matrices and free
probability, numerical algebra, combinatorics and high-dimensional
geometry, together with several novel methods and a variety of open
questions.