Part I: Foundations and Computations: Deloopings in Algebraic K- theory -- The Motivic Spectral Sequence -- K-theory of truncated polynomial algebras -- Bott Periodicity in Topological, Algebraic and Hermitian K-theory -- Algebraic K-theory of Rings and Integers in Local and Global Fields. Part II: K-theory and Algebraic Geometry: Motivic Cohomology, K-theory and topological cyclic Homology -- K-theory and Intersection Theory -- Regulators -- Algebraic K-theory, Algebraic Cycles and Arithmetic Geometry -- Mixed Motives. Part III: K-theory and Geometric Topology: Witt Groups -- K-theory and Geometric Topology -- Quadratic K-theory and Geometric Topology. Part IV: K-theory and Operator Algebras: Bivariant K-and Cyclic Theories -- The Baum-Connes and the Farrell-Jones Conjectures in K-and L-theory -- Comparison Between Algebraic and Topological K-theory for Banach Algebras and C*-Algebras. Part V: Other Forms of K-theory: Semi-topological K-theory -- Equivariant K-theory -- K(1)-local Homotopy Theory, Iwasawa Theory and Algebraic K-theory -- The K-theory of Triangulated Categories.