In modern mathematical physics, classical together with quantum, geometrical and functional analytic methods are used simultaneously. Non-commutative geometry in particular is becoming a useful tool in quantum field theories. This book, aimed at advanced students and researchers, provides an introduction to these ideas. Researchers will benefit particularly from the extensive survey articles on models relating to quantum gravity, string theory, and non-commutative geometry, as well as Connes' approach to the standard model.

In modern mathematical physics, classical together with quantum, geometrical and functional analytic methods are used simultaneously. Non-commutative geometry in particular is becoming a useful tool in quantum field theories. This book, aimed at advanced students and researchers, provides an introduction to these ideas. Researchers will benefit particularly from the extensive survey articles on models relating to quantum gravity, string theory, and non-commutative geometry, as well as Connes' approach to the standard model.

This is a review written by leading specialists on the state of the art of computational methods in lattice field theory. They cover a wide range: computer-assisted proofs, algorithms for computer simulation of field theories, effective field theories, computer studies of finite size effects, simulation with fast algorithms, and computer applicationsin experimental particle physics. The book addresses researchers, engineers, and graduate students in particle physics.