The study of nonpositively curved spaces goes back to the discovery of hyperbolic space, the work of Hadamard around 1900, and Car-tan's work in the 20's. These spaces play a signiicant role in many areas: Lie group theory, combinatorial and geometric group theory, dynamical systems, harmonic maps and vanishing theorems, geometric topology, Kleinian group theory, and Teichm uller theory. In som...