String theory and classical integrable systems

We discuss different formulations and approaches to string theory and 2d quantum gravity. The generic idea to get a unique description of many different string vacua altogether is demonstrated on the examples in 2d conformal, topological and matrix formulations. The last one naturally brings us to the appearance of classical integrable systems in string theory. Physical meaning of the appearing structures is discussed and some attempts to find directions of generalizations to "higher-dimensional" models are made. We also speculate on the possible appearence of quantum integrable structures in string theory.