Noncommutative Geometry and Physics 3 Proceedings of the Noncommutative Geometry and Physics 2008, on K-theory and D-brane, Shonan Village Center, Japan, 18-22 February 2008 ; [proceedings of the RIMS Thematic Year 2010 on Perspectives in Deformation Quantization and Noncommutative Geometry, Kyoto University, Japan, 1 April 2010-31 March 2011]

Noncommutative differential geometry has many actual and potential applications to several domains in physics ranging from solid state to quantization of gravity. The strategy is to formulate usual differential geometry in a somewhat unusual manner, using in particular operator algebras and related concepts, so as to be able to plug in noncommutativity in a natural way. Algebraic tools such as K-theory and cyclic cohomology and homology play an important role in this field.