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This two volume set presents the proceedings of the XX International Conference held in New York in 1991. It presents reports on some of the most recent advances on the interaction between differential geometry and theoretical physics. The papers are grouped into the following four broad categories: geometric methods, noncummutative geometry, quantum gravity and topological quantum field theory. A few of the topics covered are Chern-Simons theory and generalizations, knot invariants, models of 2D gravity, quantum groups and strings on black holes.