In recent years there has been remarkable progress in understanding non-perturbative dynamics of gauge fields and their relationship to string theory. Central to this progresss is the AdS/CFT correspondence (Anti de Sitter/Conformal Field Theory correspondence) which conjectures an equivalence between theories of gravity on a curved space and gauge theories defined on the boundary of such spaces. Many important developments have been made by using methods of exactly solvable (integrable) systems. This Summer School will provide an introduction to these fundamental topics.