This volume collects together the contributions of many important rese archers, including Sir Roger himself, and gives an overview of the man y applications of geometrical ideas and techniques across mathematics and the physical sciences. From the area of pure mathematics papers ar e included on the topics of classical differential geometry and non-co mmutative geometry, knot invariants, and the applications of gauge the ory. Contributions from applied mathematics cover the topics of integr able systems and general relativity. Current research in experimental and theoretical physics inspired...