Cyclic homology in non commutative geometry This volume contains contributions by three authors and treats aspects of noncommutative geometry that are related to cyclic homology. The authors give rather complete accounts of cyclic theory from different points of view. The connections between (bivariant) K theory and cyclic theory via generalized Chern characters are discussed in detail. Cyclic theory is the natural setting for a variety of general abstract index theorems. A survey of such index theorems is given and the concepts and ideas involved in these theorems are explained. TOC:I. Cyclic Theory Bivariant K Theory and the Bivariant Chern Connes Character by J. Cuntz: 1. Cyclic Theory; 2. Cyclic Theory for Locally Convex Algebras; 3. Bivariant K Theory; 4. Infinite Dimensional Cyclic Theories; A. Locally Convex Algebras; B. Standard Extensions. II. Noncommutative Geometry the Transverse Signature Operator and Hopf Algebras (after A. Connes and H. Moscovici) by G. Skandalis: 1. Preliminaries; 2. The Local Index Formula; 3. The Diff Invariant Signature Operator; 4. The Transverse Hopf Algebra. III. Cyclic Homology by B. Tsygan: 1. Introduction; 2. Hochschild and Cyclic Homology of Algebras; 3. The Cyclic Complex C{\\lambda}_{\\bullet}; 4. Non Commutative Differential Calculus; 5. Cyclic Objects; 6. Examples; 7. Index Theorems; 8. Riemann Roch Theorem for D Modules