A Symposium on Commutative Algebra was held at the University of Durham during the period 15–25 July, 1981, under the auspices of the London Mathematical Society and with financial support from the Science and Engineering Research Council. There were 71 participants.

The academic programme was built round a series of invited one hour lectures; in addition, many participants volunteered lectures at sessions of short talks. It was decided, on account of limitations of space, to restrict this volume to articles by the invited speakers related to lectures given at the Symposium, although all participants were welcome to contribute to the section of ‘Further problems’ at the end of the book. The articles have been grouped together in sections in the hope that the result will reflect the flavour of the main themes of the Symposium. The first group of papers is concerned with the local homological conjectures, big Cohen–Macaulay modules, and related topics and applications; the second group consists of articles related to determinantal ideals and finite free resolutions; and the third group is concerned with various topics in local algebra, including multiplicity theory, Hilbert and Poincare series, and associated graded rings. Within each section, the papers are arranged in alphabetical order of authors' names.

Participants at the Symposium were invited to submit open problems in commutative algebra for inclusion in a Problem Section in these proceedings, and the response to that invitation is contained in the final section of the book, entitled ‘Further problems’. I am grateful to the contributors for their efforts.