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 -- …
What is Algebra? -- Fields -- Commutative Rings -- Homomorphisms and Ideals -- Modules -- Algebraic Aspects of Dimension -- The Algebraic View of Infinitesimal Notions -- Noncommutative Rings -- Modules over Noncommutative Rings -- Semisimple Modules and Rings -- Division Algebras of Finite Rank -- The Notion of a Group -- Examples of Groups: Finite Groups -- Examples of Groups: Infinite Discre…