Random matrix theory is at the intersection of linear algebra, probability theory and integrable systems, and has a wide range of applications in physics, engineering, multivariate statistics and beyond. This volume is based on a Fall 2010 MSRI program which generated the solution of long-standing questions on universalities of Wigner matrices and beta-ensembles, and opened new research directions especially in relation to the KPZ universality class of interacting particle systems and low-rank perturbations. The book contains review articles and research contributions on all these topics, in...