An Introduction to Noncommutative Differential Geometry and its Physical Applications

This is an introduction to noncommutative geometry, with special emphasis on those cases where the structure algebra, which defines the geometry, is an algebra of matrices over the complex numbers. Applications to elementary particle physics are also discussed. This second edition is thoroughly revised and includes new material on reality conditions and linear connections plus examples from Jordanian deformations and quantum Euclidean spaces. Only some familiarity with ordinary differential geometry and the theory of fiber bundles is assumed, making this book accessible to graduate students and newcomers to this field.

"...the author has done a good job of opening the way to understanding a difficult theory...worth a look." MAA Online

"...this book provides an excellent pedagogical introduction to noncommutative geometry for mathematicians as well as physicists. The great number of examples together with the comprehensive references at the end of each chapter lead the reader directly to a large variety of results of recent research." Mathematical Reviews