**9/14, 9/21**:

- Definitions of K_0, K_1, and of higher K_i via Quillen's plus construction
- The group-completion of an H-space
- S^{-1}S as a model for the group completion of S
- The space K_0(R) x BGLR^+ is the group completion of the classifying space of the category of f.g. projective R-modules

- Arlettaz: “Algebraic K-theory of rings from a topological viewpoint”
- Quillen: “Higher K-theory for categories with exact sequences” New developments in topology (Proc. Symp. Algebraic Topology, Oxford, 1972)
- Grayson: “Higher Algebraic K-theory II”
- Weibel's K-book (available on his webpage)
- Milnor: “Introduction to Algebraic K-theory” (Annals Studies Orange Series)

- Quillen's Q construction also defines algebraic K-theory
- Properties of the Q construction
- Localization and devissage theorems

- Quillen's Computation of the K-theory of finite fields
- Adams operations and Quillen's proof of the Adams Conjecture

- Quillen: “On the cohomology and K-theory of the general linear group over a finite field”
- Quillen: “The Adams conjecture”
- Dwyer: “Quillen's work on the Adams conjecture”

- The h-cobordism theorem and pseudo-isopties
- The pseudo-isotopy space P(M) and its deloopings H(M), Wh(M)
- The Whitehead group pi_1 Wh(M) and trivializations of h-cobordisms
- Waldhausen's split exact sequence QX_+ --> A(X) --> Wh(X)
- The S_dot construction and Waldhausen's algebraic K-theory of spaces
- A(*) is K(S)

- Rognes' notes on the stable parametrized h-cobordism theorem
- Waldhausen: “Algebraic K-theory of Spaces” (SLNM 1126)
- Waldhausen: “An outline of how manifolds relate to algebraic K-theory”
- Rosenberg: “K-theory and goeometric topology” (survey article)

- The cyclic bar construction and the free loop space
- Hochschild Homology, Topological Hochschild Homology (THH)
- Cyclotomic Spectra, Topological Cyclic Homology (TC)
- The cyclotomic trace THH --> TC
- THH and TC of F_p
- K-theory of W(k)-algebras, red shift phenomena

- Madsen: “Algebraic K-theory and traces” (Current Developments in Mathematics, 1995)
- Bökstedt: “Topological Hochschild homology,” “Topological Hochschild homology of Z and Z/p” (preprints)
- Dundas, McCarthy: “ Topological Hochschild homology of ring functors and exact categories” (J. Pure Appl. Algebra 109 (1996), no. 3, 231--294)
- Blumberg, Mandell: “Localization theorems in topological Hochschild homology and topological cyclic homology” (Geom. Topol. 16 (2012), no. 2, 1053--1120)
- Bökstedt, Hsiang, Madsen: “The cyclotomic trace and algebraic K-theory of spaces” (Invent. Math. 111 (1993), no. 3, 465--539)
- Hesselholt, Madsen: “On the K-theory of finite algebras over Witt vectors of perfect fields” (Topology 36 (1997), no. 1, 29--101)
- Hesselholt, Madsen: “On the K-theory of local fields” (Ann. of Math. (2) 158 (2003), no. 1, 1--113)