Algebraic K-theory.- Finite structures.- Geometric bands.- Algebraic bands.- Localization and completion in K-theory.- K-theory of polynomial extensions.- K-theory of formal power series.- Algebraic transversality.- Finite domination and Novikov homology.- Noncommutative localization.- Endomorphism K-theory.- The characteristic polynomial.- Primary K-theory.- Automorphism K-theory.- Witt vectors.- The fibering obstruction.- Reidemeister torsion.- Alexander polynomials.- K-theory of Dedekind rings.- K-theory of function fields.- Algebraic L-theory.- Algebraic Poincaré complexes.- Codimension q surgery.- Codimension 2 surgery.- Manifold and geometric Poincaré bordism of X × S 1.- L-theory of Laurent extensions.- Localization and completion in L-theory.- Asymmetric L-theory.- Framed codimension 2 surgery.- Automorphism L-theory.- Open books.- Twisted doubles.- Isometric L-theory.- Seifert and Blanchfield complexes.- Knot theory.- Endomorphism L-theory.- Primary L-theory.- Almost symmetric L-theory.- L-theory of fields and rational localization.- L-theory of Dedekind rings.- L-theory of function fields.- The multisignature.- Coupling invariants.- The knot cobordism groups.

Bringing together many results previously scattered throughout the research literature into a single framework, this work concentrates on the application of the author's algebraic theory of surgery to provide a unified treatment of the invariants of codimension 2 embeddings, generalizing the Alexander polynomials and Seifert forms of classical knot theory.