Table of Contents of Volume I Invited Lectures (Part 1).- Plenary Lectures.- The Vassiliev Theory of Discriminants and Knots.- Transparent Proofs and Limits to Approximation.- Poisson Algebraic Groups and Representations of Quantum Groups at Roots of 1.- Gauge Theory and Four-Manifold Topology.- Spectral Theory and Geometry.- Pattern Theory: A Unifying Perspective.- Brownian Motion and Obstacles.- Geometric Quantization and Equivariant Cohomology.- Parallel Lectures.- The Power of Exponentiation in Arithmetic.- Subspace Arrangements.- Optimal Recovery of Functions and Integrals.- Existence globale et diffusion pour les modèles discrets de la cinétique des gaz.- Sporadic Groups and String Theory.- A Harmonic Analysis Approach to Problems in Nonlinear Partial Differential Equations.- (Some) Old and New Results on Algebraic Surfaces.- Evidence for a Cohomological Approach to Analytic Number Theory.- Cauchy-Riemann Operators, Self-Duality, and the Spectral Flow.- Index of Authors of Volumes I and II.