Since K. Wilson's seminal work on lattice gauge theory in 1974 the regularization of quantum field theories by a space–time lattice has become one of the basic methods for non-perturbative studies in field theory. It has been applied to Quantum Chromodynamics, to the electroweak theory, and to various other model field theories. Many techniques have been developed to deal with quantum fields on a lattice, and with their help many insights into non-perturbative phenomena have been gained.

During a workshop in Cargèse in 1989 Peter Landshoff explained to us his impression that the development of this subject in recent years justified a new book after the one by Michael Creutz on lattice gauge theory, which was published by Cambridge University Press in 1983, and he invited us to undertake the task of writing a book about lattice field theory. As usual the writing took more time than anticipated by the authors and was only finished three years later.

The resulting book is by no means homogeneous, which corresponds to our intentions and also reflects the continuous but irregular development of the field. Some parts are of a more introductory nature and may be useful for graduate students who would like to enter the field. Other parts explain specific techniques in some detail and may serve as a reference for active workers on the subject. Still other parts summarize some of the results obtained about particular questions, or can be used as a guide to the literature.