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Lectures on Algebraic K theory by J.F. Jardine
This note covers the following topics: Some homotopy theory, Exact categories, Q-construction, Fundamental groupoid, Waldhausen's constructions, Additivity, The K-theory spectrum, Products, Group completion, Q=+ theorem, The defining acyclic map, Homotopy fibres, Resolution theorem, Dévissage, Abelian category localization, Coherent sheaves and open subschemes, Product formulas, K-theory with finite coefficients, Homology, K-theory of graded rings, Homotopy property, Rigidity, K-theory of finite fields.
Author(s): J.F. Jardine
NA Pages 
The local structure of algebraic K theory
This note explains the following topics: Algebraic K-theory, Gamma-spaces and S-algebra, Reductions, Topological Hochschild homology, The trace K, Topological Cyclic homology, The comparison of K-theory and TC, Homotopical foundations.
Author(s): Bjorn Ian Dundas, Thomas G. Goodwillie and Randy McCarthy
424 Pages
Characteristic classes and K theory
This note descibes the following topics: Vector bundles, Characteristic classes, K-theory, The functor K, The fundamental product theorem, The Mayer–Vietoris sequence, Structure of K-theory, The yoga of symmetric polynomials.
Author(s): Oscar Randal-Williams
62 Pages
K theory For Operator Algebras
This note will develop the K-theory of Banach algebras, the theory of extensions of C algebras, and the operator K-theory of Kasparov from scratch to its most advanced aspects. Topics covered includes: Survey of Topological K-Theory, Operator K-Theory, Preliminaries, K-theory Of Crossed Products, Theory Of Extensions, Kasparov’s Kk-theory.
Author(s): Bruce Blackadar
314 Pages
A Geometric Introduction To K Theory
This is one day going to be a textbook on K-theory, with a particular emphasis on connections with geometric phenomena like intersection multiplicities.
Author(s): Daniel Dugger
285 Pages
This note provides an overview of various aspects of algebraic K-theory, with the intention of making these lectures accessible to participants with little or no prior knowledge of the subject.
Author(s): Eric Friedlander
78 Pages
Lectures on K theory (PDF 95P)
This lecture note covers the following topics: beginning of K theory, K theory of Banach algebras, Applications of topological Ktheory, The Atiyah- Singer index theorem, Algebraic K theory of Bass and Milnor applications, Higher Algebraic K theory, Hermitian K theory, Cyclic homology and K theory.
Author(s): Max Karoubi
95 Pages
Lectures on Topics in Algebraic K Theory (PDF 138P)
This note covers the following topics: The exact sequence of algebraic K-theory, Categories of modules and their equivalences, Brauer group of a commutative ring, Brauer-Wall group of graded Azumaya algebras and The structure of the Clifford Functor.
Author(s): Hyman Bass
138 Pages
Lecture Notes on Algebraic K Theory (PDF 252P)
This book covers the following topics: Categories and functors, Transformations and equivalences, Universal properties, Homotopy theory, Homotopy theory of categories, Waldhausen K-theory, Quillen K-theory, Abelian and exact categories.
Author(s): John Rognes
252 Pages
This note introduces the definitions of the K-theory groups such as The group K0, The group K1, The group K2 and Higher K-theory groups.
Author(s): Olivier Isely
45 Pages
This book focusing on topological K-theory and containing also the necessary background material on vector bundles and characteristic classes.
Author(s): Allen Hatcher
NA Pages
An introduction to algebraic K Theory
This book covers the following topics: Projective Modules and Vector Bundles, The Grothendieck group K_0, K_1 and K_2 of a ring, higher K-theory, The Fundamental Theorems of higher K-theory and the higher K-theory of Fields.
Author(s): Charles Weibel
NA Pages
The K book An Introduction to Algebraic K theory
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Author(s): NA
NA Pages
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Author(s): NA
NA Pages
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