Cyclic homology was introduced independently by A. Connes (whose motivation comes from K-homology and index pairing with K-theory) and by B. Tsygan (who was motivated by algebraic K-theory and Lie algebra cohomology). The book contains three contributions. The first one, by J. Cuntz, discusses basic aspects of cyclic theory with emphasis on closely related topological K-theory, bivariant K-theory, and locally convex and m-algebras. The second contribution, by B. Tsygan, studies various algebraic structures on Hochschild and cyclic cochains and homologies. The third contribution, written by G. Skandalis, explains some aspects of cyclic cohomology related to operator theoretic index formula (e.g. the transversal signature operator) and diffeomorphism invariant pseudodifferential calculus.