Algebraic K-theory is a modern branch of algebra which has many important applications in fundamental areas of mathematics connected with algebra, topology, algebraic geometry, functional analysis and algebraic number theory. Methods of algebraic K-theory are actively used in algebra and related fields, achieving interesting results.
This book presents the elements of algebraic K-theory, based essentially on the fundamental works of Milnor, Swan, Bass, Quillen, Karoubi, Gersten, Loday and Waldhausen. It includes all principal algebraic K-theories,...

While in classical (abelian) homological algebra additive functors from abelian (or additive) categories to abelian categories are investigated, non- abelian homological algebra deals with non-additive functors and their homological properties, in particular with functors having values in non-abelian categories. Such functors haveimportant applications in algebra, algebraic topology, functional analysis, algebraic geometry and other principal areas of mathematics. To study homological properties of non-additive functors it is necessary to define and investigate their derived functors and...