The 'algebraic K-theory presented here is, essentially, a part of general linear algebra. It is concerned with the structure theory of projective modules, and of their automorphism groups. Thus, it is a generalization, in the most naive sense, off the theorem asserting the existence and uniqueness of bases for vector spaces, and of the group theory of the general linear group over a field. One witnesses here the evolution of these theorems as the base ring becomes more general than a field. There is a "stable form" in which the above theorems survive (Part2). In a stricter sense these theorems fail in the general case, and the Grothendieck groups (k0) and Whitehead groups (k1) which we study can be viewed as providing a measure of their failure. A topologist can similarly seek such generalization of hte structure theorems of linear algebra. He views a vector space as a special case of a vector bundle. The homotopy theory of vector bundles, and topological k-theory, then provide a completely satisfactory framework within which to treat such questions. It is remarkable that there exists, in algebra, nothing remotely comparable depth or generality, even though many of these questions are algebraic in character. --- excerpt from book's Introduction
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