This volume presents articles originating from invited talks at an exciting international conference held at The Fields Institute in Toronto celebrating the sixtieth birthday of the renowned mathematician, Vladimir Arnold. Experts from the world over - including several from 'Arnold's school' - gave illuminating talks and lively poster sessions. The presentations focussed on Arnold's main areas of interest: singularity theory, the theory of curves, symmetry groups, dynamical systems, mechanics, and related areas of mathematics. The book begins with notes of three lectures by V. Arnold given in the framework of the Institute's Distinguished Lecturer program.The topics of the lectures are: From Hilbert's Superposition Problem to Dynamical Systems; Symplectization, Complexification, and Mathematical Trinities; and, Topological Problems in Wave Propagation Theory and Topological Economy Principle in Algebraic Geometry. Arnold's three articles include insightful comments on Russian and Western mathematics and science. Complementing the first is Jurgen Moser's 'Recollections', concerning some of the history of KAM theory.