This three-year award supports U.S.-France cooperative research in Theoretical Physics between Antal Jevicki of Brown University and Jean Avan of the Laboratory for Theoretical High Energy Physics, University of Paris VI. The investigators propose to solve a series of problems in string theory and quantum gravity. The objectives are to understand the symmetries of two dimensional string theory and explore its relationship to higher dimensional integrable theories. Specifically the research involves exotic matrix models, quantum symmetries, interacting theory of tachyons, topological fields and the nature of w- infinity algebra, which appears throughout matrix models and topological fields. The U.S. investigator brings to this collaboration expertise in theoretical physics. This is complemented by the French investigators experience in mathematical physics. The investigators have already progressed on some key aspects of string theory and the nature of w-infinity algebra. This project will enable them to expand their efforts and ultimately apply their results to the physics of black holes, early cosmology, and ultra high energy physics.