``An introduction to algebraic K-theory''

1. Free and stably free modules; p.1
2. Projective modules; p.6
3. The Picard group of a ring; p.15
4. Topological vector bundles and Chern classes; p.26
5. Algebraic vector bundles. p.38

1. group completion of a monoid; p.1
2. K_0 of a ring; p.5
3. K(X) of a topological space; p.17
4. Lambda and Adams operations; p.23
5. K_0 of a symmetric monoidal category; p.36
6. K_0 of an abelian category; p.44
7. K_0 of an exact category; p.58
8. K_0 of schemes and varieties; p.72
9. K_0 of a Waldhausen category; p.82
Appendix: localizing by categories of fractions. p.96

1. K_1 of a ring; p.1
2. Relative K_1; p.12
3. the Fundamental Theorems for K_1 and K_0; p.16
4. Negative K-theory; p.26
5. Milnor's K_2 of a ring; p.32
6. K_2 of fields; p.44
7. Milnor K-theory of fields. p.57

1. BGL+ constructions; p.2
2. Geometric realization of a small category; p.11
3. Group completions for symmetric monoidal categories; p.21
4. Quillen's Q-construction for exact categories; p.32
5. The ``+=Q'' theorem; p.36
6. Waldhausen's wS. construction; p.40
7. The Gillet-Grayson construction; p.47
8. Karoubi-Villamayor K-theory; p.50
9. Homotopy K-theory; p.56
10 K-theory with finite coefficients; p.58.

Watch it grow like Topsy!

• Chapter V: The Fundamental Theorems
  1. The Additivity theorem;
  2. Changes in Waldhausen Structure;
  3. The Resolution Theorem; 4. Devissage;
  Localization Sequences for G_*; Localization sequences for K-theory
  (Here's the Trieste Lecture IV on this)

• Chapter VI: Higher K-theory of Fields
  (Here's the Trieste Lecture VIII on this)

• Chapter VII: Applications to Algebraic Geometry

• Chapter VIII: Higher Chow Groups and Motivic Cohomology
  (Here are the Trieste Lecture IX and Lecture X on this)

• References

Suggestions are welcome!

Thanks for corrections go to:

Errata for Jon Rosenberg's 1994 book on K-theory