• Frontmatter,
• Preface and Guide to the Literature,
• Contents,
• §1. Projective Modules and K0¿,
• §2 . Constructing Projective Modules,
• §3. The Whitehead Group K1¿,
• §4. The Exact Sequence Associated with an Ideal,
• §5. Steinberg Groups and the Functor K2,
• §6. Extending the Exact Sequences,
• §7. The Case of a Commutative Banach Algebra,
• §8. The Product K1¿ ¿ K1¿ ¿ K2¿,
• §9. Computations in the Steinberg Group,
• §10. Computation of K2Z,
• §11. Matsumoto's Computation of K2 of a Field,
• 12. Proof of Matsumoto's Theorem,
• §13. More about Dedekind Domains,
• §14. The Transfer Homomorphism,
• §15. Power Norm Residue Symbols,
• §16. Number Fields,
• Appendix. Continuous Steinberg Symbols,
• Index,

Algebraic K-theory describes a branch of algebra that centers about two functors. K0 and K1, which assign to each associative ring ¿ an abelian group K0¿ or K1¿ respectively. Professor Milnor sets out, in the present work, to define and study an analogous functor K2, also from associative rings to abelian groups. Just as functors K0 and K1 are important to geometric topologists, K2 is now considered to have similar topological applications. The exposition includes, besides K-theory, a considerable amount of related arithmetic.