  This article is an introductory review of random matrix theory (RMT) and its
applications, with special focus on quantum chaos. Random matrices were first
used by Wigner to understand the spectra of complex nuclei from a statistical
perspective. Subsequently there have been novel applications to diverse areas,
e.g., atomic and molecular physics, mesoscopic and nanoscopic systems,
microwave cavities, econophysics, biological sciences, communication theory.
This article is designed to be accessible at the graduate and post-doctoral
level.
