This book is the fruit of the London Mathematical Society Symposium on ‘L-functions and Arithmetic’, which was held at the University of Durham from June 30 until July 11, 1989. The Symposium attempted to bring together the many and diverse aspects of number theory and arithmetical algebraic geometry which are currently being studied under the general theme of the connections between L-functions and arithmetic. In particular, there were series of lectures on each of the following topics:

1. (i) descent theory on elliptic curves;

2. (ii) automorphic L-functions;

3. (iii) Beilinson's conjectures;

4. (iv) p-adic cohomology and the Bloch-Kato conjectures on the Tamagawa numbers of motives;

5. (v) Iwasawa theory of motives;

6. (vi) l-adic representations attached to automorphic forms;

7. (vii) L-functions and Galois module structure of rings of integers and groups of units.

While the editors were not able to persuade all the lecturers to write up the material of their lectures, the present volume represents a major portion of the proceedings of the Symposium. The editors wish to express their warm appreciation to all the lecturers. The Symposium was sponsored by the London Mathematical Society, and benefited from the generous financial support of the Science and Engineering Research Council. We are grateful to Tony Scholl and the Department of Mathematics of the University of Durham for their help in organising the meeting; we particularly wish to thank Grey College for its kind hospitality.