Geometric construction of N=2 gauge theories

In this lecture we give a brief, elementary introduction to the natural realization of non-perturbative N = 2 quantum field theories as a low energy limit of classical string theory. We review the systematic construction of six, five, and four dimensional gauge theories using geometrical data, which provides also the exact, non-perturbative solution via mirror symmetry. This construction has lead to the exact solution of a large class of gravity free gauge theories, including Super Yang Mills (SYM) theories as well as non-conventional quantum field theories without a known Lagrangian description.