Table of contents: Plenary Lectures - V.I. Arnold: The Vassiliev Theory of Discriminants and Knots - L. Babai: Transparent Proofs and Limits to Approximation - C. De Concini: Poisson Algebraic Groups and Representations of Quantum Groups at Roots of 1 - S.K. Donaldson: Gauge Theory and Four-Manifold Topology - W. Müller: Spectral Theory and Geometry - D. Mumford: Pattern Theory: A Unifying Perspective - A.-S. Sznitman: Brownian Motion and Obstacles - M. Vergne: Geometric Quantization and Equivariant Cohomology - Parallel Lectures - Z. Adamowicz: The Power of Exponentiation in Arithmetic - A. Björner: Subspace Arrangements - B. Bojanov: Optimal Recovery of Functions and Integrals - J.-M. Bony: Existence globale et diffusion pour les modèles discrets - R.E. Borcherds: Sporadic Groups and String Theory - J. Bourgain: A Harmonic Analysis Approach to Problems in Nonlinear Partial Differatial Equations - F. Catanese: (Some) Old and New Results on Algebraic Surfaces - Ch. Deninger: Evidence for a Cohomological Approach to Analytic Number Theory - S. Dostoglou and D.A. Salamon: Cauchy-Riemann Operators, Self-Duality, and the Spectral Flow