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Noncommutative differential geometry is a new approach to classical geometry. It was originally used by Fields Medalist A. Connes in the theory of foliations, where it led to striking extensions of Atiyah-Singer index theory. It also may be applicable to hitherto unsolved geometric phenomena and physical experiments. However, noncommutative differential geometry was not well understood even among mathematicians. Therefore, an international symposium on commutative differential geometry and its applications to physics was held in Japan, in July 1999. Topics covered included: deformation problems, Poisson groupoids, operad theory, quantization problems, and D-branes. The meeting was attended by both mathematicians and physicists, which resulted in interesting discussions. This volume contains the refereed proceedings of this symposium. Providing a state of the art overview of research in these topics, this book is suitable as a source book for a seminar in noncommutative geometry and physics.

Noncommutative differential geometry --- Mathematical physics --- Géométrie différentielle non commutative --- Physique mathématique --- Elementary particles (Physics). --- Quantum field theory. --- Differential geometry. --- Quantum physics. --- Integral transforms. --- Operational calculus. --- Global analysis (Mathematics). --- Manifolds (Mathematics). --- Elementary Particles, Quantum Field Theory. --- Differential Geometry. --- Quantum Physics. --- Integral Transforms, Operational Calculus. --- Global Analysis and Analysis on Manifolds. --- Geometry, Differential --- Topology --- Analysis, Global (Mathematics) --- Differential topology --- Functions of complex variables --- Geometry, Algebraic --- Operational calculus --- Differential equations --- Electric circuits --- Integral equations --- Transform calculus --- Transformations (Mathematics) --- Quantum dynamics --- Quantum mechanics --- Quantum physics --- Physics --- Mechanics --- Thermodynamics --- Differential geometry --- Relativistic quantum field theory --- Field theory (Physics) --- Quantum theory --- Relativity (Physics) --- Elementary particles (Physics) --- High energy physics --- Nuclear particles --- Nucleons --- Nuclear physics --- Géométrie différentielle non commutative. --- Physique mathématique. --- Noncommutative differential geometry - Congresses. --- Mathematical physics - Congresses. --- Géométrie différentielle non commutative. --- Physique mathématique.