I Conformally Invariant Field Theories, Integrability, Quantum Groups -- Z/NZ Conformal Field Theories -- Affine Characters and Modular Transformations -- Conformal Field Theory on a Riemann Surface -- Modular Invariance of Field Theories and String Compactifications -- Yang-Baxter Algebras and Quantum Groups -- Representations of Uq sl(2) for q a Root of Unity -- II Quasicrystals and Related Geometrical Structures -- Some Quasiperiodic Tilings as Modulated Lattices -- Types of Order and Diffraction Spectra for Tilings of the Line -- A Topological Constraint on the Atomic Structure of Quasicrystals -- From Approximants to Quasicrystals: A Non-standard Approach -- The Topological Structure of Grain Boundaries -- Calculation of 6D Atomic Surfaces from a Given Approximant Crystalline Structure Using Approximate Icosahedral Periodic Tilings -- III Spectral Problems, Automata and Substitutions -- Spectral Properties of Schrödinger's Operator with a Thue-Morse Potential -- On the Non-commutative Torus of Real Dimension Two -- Topological Invariants Associated with Quasi-Periodic Quantum Hamiltonians -- Spectra of Some Almost Periodic Operators -- The Quantum Hall Effect and the Schrödinger Equation with Competing Periods -- Finite Automata in 1-D and 2-D Physics -- Summation Formulae for Substitutions on a Finite Alphabet -- The Inhomogeneous Ising Chain and Paperfolding -- IV Dynamical and Stochastic Systems -- A Nonlinear Evolution with Travelling Waves -- Iterating Random Maps and Applications -- Hannay Angles and Classical Perturbation Theory -- Nekhoroshev Stability Estimates for Symplectic Maps and Physical Applications -- p-adic Dynamical Systems -- V Further Arithmetical Problems, and Their Relationship to Physics -- Dirichlet Series Associated with a Polynomial -- Some Remarks on Random Number Generators -- Bounds for Non-blocking Switch Networks -- The Ising Model and the Diophantine Moment Problem -- Statistical Theory of Numbers -- Algebraic Number Theory and Hamiltonian Chaos -- Semiclassical Properties of the Cat Maps -- Index of Contributors.