Foreword to the first edition (1970) This book is being published in the form in which it was originally planned and written. In some ways, this is not satisfactory: the demands made on the reader are rather heavy, though this is partly also due to a systematic attempt at completeness ('simplified' proofs have appeared of some of my results, but in most cases the simplification comes primarily from a loss of generality). However, the partly historical presentation adopted here has its advantages: the reader can see (particularly in §5 and §6) how the basic problem of surgery leads to algebra, before meeting the abstract presentation in §9. Indeed, this relation of geometry to algebra is the main theme of the book. I have not in fact emphasised the algebraic aspects of the L-groups, though this is mentioned where necessary in the text: in particular, I have omitted the algebraic details of the calculations of the L-groups, since this is lengthy, and needs a different background. Though some rewriting is desirable (I would prefer to recast several results in the framework suggested in §17G also, some rather basic results were discovered too late to be fully incorporated at the appropriate points - see the footnotes and Part 4) this would delay publication indefinitely, so it seemed better for the book to appear now, and in this form. Chapters 0-9 were issued as duplicated notes from Liverpool University in Spring, 1967. They have been changed only by correcting minor errors, adding §1A (which originated as notes from Cambridge University in 1964), and cor- recting a mistake in the proof of (9.4). Part 2 was issued (in its present form) as duplicated notes from Liverpool University in May 1968. The rest of the material appears here for the first time. Foreword to the second edition It is gratifying to learn that there is still sufficient interest in this book for it to be worth producing a new edition. Although there is a case for substan- tially rewriting some sections, to attempt this would have delayed production indefinitely. I am thus particularly pleased that Andrew Ranicki has supplemented the original text by notes which give hints to the reader, indicate relevant subsequent developments, and say where the reader can find accounts of such newer results. He is uniquely qualified to do this, and I am very happy with the result. The first edition appeared before the days of T^X, so the entire manuscript had to be re-keyed. I am grateful to Iain Rendall for doing this efficiently and extremely accurately. C. T. C. Wall, Liverpool, November 1998. ix

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