代数K理论在代数拓扑、数论、代数几何和算子理论等现代数学各个领域中的作用越来越大。这门学科的广泛性往往使人感觉望而生畏。本书以1990年秋天Maryland大学讲义为基础，不仅为数学领域研究生提供很好的学习代数K理论的基本知识，也讲述其在各个领域的应用。全书结构完整，了解代数基础知识、基本代数拓扑和几何拓扑知识就可以完全读懂这本书。该书也涉及到不少代数拓扑、拓扑代数和代数数论的知识。最后一章简明地介绍了循环同调以及其与K理论的关系。目次：环的K0群；环的K1群；范畴的K0、K1群，MilnorK2群；QuillenK理论和+-结构；循环同调及其与K理论的关系。 读者对象：数学系高年级学生及研究生的教材，也可供高校数学教师及数学研究人员阅读或参考。 Algebraic K-theory is the branch of algebra dealing with linear algebra （especially in the limiting case of large matrices） over a general ring R instead of over a field. It associates to any ring R a sequence of abelian groups Ki（R）. The first two of these， K0 and K1， are easy to describe in concrete terms， the others are rather mysterious. For instance， a finitely generated projective R-module defines an element of K0（R）， and an invertible matrix over R has a "determinant" in K1（R）. The entire sequence of groups K1（R） behaves something like a homology theory for rings. Algebraic K-theory plays an important role in many areas， especially number theory， algebraic topology， and algebraic geometry. For instance， the class group of a number field is essentially K0（R）， where R is the ring of integers， and "Whitehead torsion" in topology is essentially an element of K1（Zπ）， where π is the fundamental group of the space being studied. K-theory in algebraic geometry is basic to Grothendieck's approach to the Riemann-Roch problem. Some formulas in operator theory， involving determinants and determinant pairings， are best understood in terms of algebraic K-theory. There is also substantial evidence that the higher K-groups of fields and of rings of integers are related to special values of L-functions and encode deep arithmetic information. '
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