This book is the English version of the French "Geometrie non commutative" published by InterEditions Paris (1990). After the excellent initial translation by S.K. Berberian, a considerable amount of rewriting was done and many additions made, multiplying by 3.8 the size of the original manuscript. In particular the present text contains several unpublished results.

PREFACE

INTRODUCTION

Ⅰ. NONCOMMUTATIVE SPACES AND MEASURE THEORY

Ⅱ. TOPOLOGY AND K-THEORY

Ⅲ. CYCLIC COHOMOLOGY AND DIFFERENTIAL GEOMETRY

Ⅳ. QUANTIZED CALCULUS

Ⅴ. OPERATOR ALGEBRAS

Ⅵ. THE METRIC ASPECT OF NONCOMMUTATIVE GEOMETRY

BIBLIOGRAPHY

NOTATION AND CONVENTIONS

INDEX