K-theory is an interesting blend of algebra and geometry. Originally defined for (vector bundles over) topological spaces it is now also defined for (modules over) rings, giving extra algebraic information about those objects.
Most of the geometric K-theory is treated with Algebraic Topology
See also 16E20, 18F25
K-Theory is the smallest of the 61 active areas of the MSC scheme: only 515 papers with primary classification 19-XX during 1980-1997. But the area 19-XX was only available as a primary classification for Math Reviews papers starting with MR96; hence the count above is an undercount of the true size of the field. (Even granting this, however, K-theory is a fairly small field.)
Browse all (old) classifications for this area at the AMS.
"Reviews in K-theory, 1940--84", edited by Bruce A. Magurn, American Mathematical Society, Providence, 1985, 811 pp., ISBN 0-8218-0088-4
Online chapters of a book-in-progress [Charles Weibel]