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K理论在几何学领域有两个不同的起源。第一个是与拓扑学中的困难问题相关的。起点是引进怀特海挠率，这项工作始于20世纪60年代。另一个起源与拓扑K理论一样，也是开始于格罗唐迪克在1957年给出的广义黎曼一罗赫定理的证明。美国数学家巴斯1964年研究格罗唐迪克引用的K群的构造，由此开创了代数K理论的研究。其著作《代数K理论》(1968)的问世标志着代数学的这个新分支的诞生。巴斯引进了K0，并与他人合作广泛地研究K0和K1.K2是米尔诺引进的，而高阶K理论是由奎伦和其他人从各种不同观点构造的。奎伦首先解决了代数K理论中的亚当斯猜想(1970)，之后又得到K理论中塞尔猜想的证明(1976)，并开始将代数归结为拓扑，形成代数K理论的基础。代数K理论产生之后，立即应用于环论、同调代数、范畴论与线性群的理论。

Product Description
These notes are based on the course of lectures I gave at Harvard in the fall of 1964. They constitute a self-contained account of vector bundles and K-theory assuming only the rudiments of point-set topology and linear algebra. One of the features of the treatment is that no use is made of ordinary homology or cohomology theory. In fact, rational cohomology is defined in terms of K-theory.

内容截图：

1. Vector Bundles

2. K-theory

3. Operations

Appendix

ed2k://|file|K-Theory%2C.M..Atiyah%2C.Benjamin%2C.1967.djvu|6819304|9982b569ad71e2d04a68f0d14f3a074f|h=47zzmfkntefgl46n4l3wao47clq5mjnp|/
ed2k://|file|Baum%2C.Cortinas%2C.Meyer%2C.et.al%2C.Topics.in.Algebraic.and.Topological.K-Theory%2C.LNM.2008%2C.Springer%2C.2010.pdf|2544923|c7e7ac42432f2bfa283eee7871a01993|h=kzd4pifqahkz2hnhtbmmzvsqx3qeziys|/
ed2k://|file|Nonabelian.Algebraic.Topology.Filtered.Spaces%2C.Crossed.Complexes%2C.Cubical.Homotopy.Groupoids%2C.Brown%2C.Higgins%2C.Sivera.%2C.EMS%2C.2011.pdf|7021722|9d91559addfe8b7864b2f9b22bdada0d|h=catkouxada2su7vjofnlrg572yfpkhu3|/
ed2k://|file|Representation.Theory.and.Higher.Algebraic.K-Theory%2C.Aderemi.Kuku%2C.CRC%2C.2007.pdf|3331496|7faef6f0b087dac80991192fd597a0b2|h=xjlibokx2dkop55v2byoldhnefgfxgu5|/
ed2k://|file|Noncommutative.Geometry.and.Physics.Renormalisation%2C.Motives%2C.Index.Theory%2C.Carey%2C.EMS%2C.2011.pdf|2137371|1f9e05e782109e59cdbd87271048f8d5|h=65ktmciujyg5yrkhahb4ctnlbdi4rxa5|/
ed2k://|file|Complex.Topological.K-Theory%2C.Efton.Park%2C.CUP%2C.2008.pdf|1316213|d7c2e93b376904a40be00fa3ffab8f0f|h=eefzywcsswdk4wgqhobtf7lu3mg7ox6h|/