Higher algebraic K-theory : an overview / E. Lluis-Puebla, J. L. Loday, H. Gillet, ... [et al.]

This volume is a compilation of the authors' papers based on lectures given at the Universidad Nacional Autónoma de México in 1985. These are expository articles, set out to describe various aspects of K-theory at a reasonably elementary level. Their titles more or less coincide with their content: Lluis-Puebla, "Introduction to algebraic K-theory''; Loday, "Introduction to algebraic K-theory and cyclic homology''; Gillet, "Comparing algebraic and topological K-theory''; Soulé, "K-theory of the integers''; Snaith, "Applications of group cohomology to bilinear forms''.
It has taken a long time for this volume to appear, and it shows, for example, in an under-emphasis of the strength of the Gabber rigidity theorem in the Gillet and Soulé articles. The subject of Snaith's article has undergone something of a sea change in the intervening years, and the volume necessarily lacks a proper appreciation of the work of Thomason, Merkurʹev and Suslin, Kato and Saito, and many others. Nevertheless, these articles are a useful addition to the K-theory literature, especially for either graduate students or research workers new to various aspects of the field. ... (MathSciNet)