Quantum field theories with local gauge symmetry are building blocks of the modern theory of fundamental interactions between elementary particles. The basic example is Quantum Chromo Dynamics. There is strong evidence that QCD is the correct theory of strong interactions, but it has been difficult to use it to account for many hadronic phenomena which is due to large value of gauge coupling at low energies. Theoretical understanding of gauge theory dynamics at large values of coupling when one cannot use the Feynman diagram perturbation theory is a major problem of physics of strong interactions. Goals include analytic computation of mass spectrum of hadrons, etc. The general aim of this proposal is to develop new theoretical tools to describe strongly coupled gauge theories. Research in the last decade brought strong evidence that connection of gauge theories to string theory should be a key to solution of this problem. Gauge-string duality and, in particular, Anti deSitter / conformal field theory (AdS/CFT) correspondence is one of the most active directions of current work in theory of fundamental interactions. A remarkable progress was achieved towards quantitative understanding of this relation in the most symmetric case of maximally supersymmetric gauge theory in flat 4 dimensions dual to superstring theory in curved 10-dimensional AdS5 x S5 space. We propose a detailed study of this duality from the string theory side using world-sheet methods and hidden integrability of the maximally symmetric theory. The goal is to provide a first-principles proof of the duality for the spectrum of states and also to establish its validity at the level of correlation functions of conformal operators. We also plan to extend string-theoretic approach to gauge-string duality to less symmetric cases, corresponding, in particular, to certain non-supersymmetric conformal and n=1 supersymmetric non-conformal planar gauge theories.