Higher Algebraic K-Theory: an overview [electronic resource] / by Emilio Lluis-Puebla, Jean-Louis Loday, Henri Gillet, Christophe Soulé, Victor Snaith.

to algebraic K-theory -- to algebraic K-theory and cyclic homology -- Comparing algebraic and topological K-theory -- Algebraic K-theory of the integers -- Applications of group cohomology to bilinear forms.

This book is a general introduction to Higher Algebraic K-groups of rings and algebraic varieties, which were first defined by Quillen at the beginning of the 70's. These K-groups happen to be useful in many different fields, including topology, algebraic geometry, algebra and number theory. The goal of this volume is to provide graduate students, teachers and researchers with basic definitions, concepts and results, and to give a sampling of current directions of research. Written by five specialists of different parts of the subject, each set of lectures reflects the particular perspective ofits author. As such, this volume can serve as a primer (if not as a technical basic textbook) for mathematicians from many different fields of interest.