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...