This is a volume of papers in honour of Peter Swinnerton-Dyer's 75th birthday; we very much regret that it appears a few months late owing to the usual kind of publication delays. This preface contains four sections of reminiscences, attempting the impossible task of outlining Peter's many-sided contributions to human culture. Section 5 is the editor's summary of the 12 papers making up the book, and the preface ends with a bibliographical section of Peter's papers to date.

Peter's first sixty years in Mathematics by Bryan Birch

Peter Swinnerton-Dyer wrote his first paper as a young schoolboy just 60 years ago, under the abbreviated name P. S. Dyer; in it, he gave a new parametric solution for x4 + y4 = z4 + t4. It is very appropriate that his first paper was on the arithmetic of surfaces, the theme that recurs most often in his mathematical work; indeed, for several years he was almost the only person writing substantial papers on the subject; and he is still writing papers about the arithmetic of surfaces sixty years later. Peter went straight from school to Trinity College (National Service had not quite been introduced); after his BA, he began research as an analyst, advised by J E Littlewood.