Random matrix theory was originally formulated by Eugene Wigner
in the fifties in the studies of quantum multi-body systems.
Random matrix theory was a revolutionary idea which provided
a completely new way of approaching problems on the junction
of quantum and statistical physics. The importance of the theory
was not immediately recognized by the community.
A break-through came with the book by Mehta and
the seminal papers by Dyson and by Brezin, Itzykson, Parisi and Zuber.
Ever since random matrix theory has continuously attracted
a great attention of a broad community of researchers.
Today it provides a universal language and a way of thinking which
applies to a wide spectrum of problems ranging from fundamental problems in:
number theory, string theory, gravity, QCD, quantum chaos,
quantum transport, information theory, combinatorics,
to applied ones as those encountered in biophysics, econophysics,
quantitative finance and telecommunication. In the talk we will
survey some applications of this theory.