Quadratic and Hermitian Forms over Rings

I. Hermitian Forms over Rings.-
1. Rings with Involution.-
2. Sesquilinear and Hermitian Forms.-
3. Hermitian Modules.-
4. Symplectic Spaces.-
5. Unitary Rings and Modules.-
6. Hermitian Spaces over Division Rings.-
7. Change of Rings.-
8. Products of Hermitian Forms.-
9. Morita Theory for Hermitian Modules.-
10. Witt Groups.-
11. Cartesian Diagrams and Patching of Hermitian Forms.- II. Forms in Categories.-
1. Additive Categories.-
2. Categories with Duality.-
3. Transfer.-
4. Reduction.-
5. The Theorem of Krull-Schmidt for Additive Categories.-
6. The Krull-Schmidt Theorem for Hermitian Spaces.-
7. Some Applications.- III. Descent Theory and Cohomology.-
1. Descent of Elements.-
2. Descent of Modules and Algebras.-
3. Discriminant Modules.-
4. Quadratic Algebras.-
5. Azumaya Algebras.-
6. Graded Algebras and Modules.-
7. Universal Norms.-
8. Involutions on Azumaya Algebras.-
9. The Pfaffian.- IV. The Clifford Algebra.-
1. Construction of the Clifford Algebra.-
2. Structure of the Clifford Algebra, the Even Rank Case.-
3. Structure of the Clifford Algebra, the Odd Rank Case.-
4. The Discriminant and the Arf Invariant.-
5. The Special Orthogonal Group.-
6. The Spinors.-
7. Canonical Isomorphisms.-
8. Invariants of Quadratic Spaces.-
9. Quadratic Spaces with Trivial Arf Invariant.- V. Forms of Low Rank.-
1. Quadratic Modules of Rank 1.-
2. Quadratic Modules of Rank 2.-
3. Quadratic Modules of Rank 3.-
4. Quadratic Modules of Rank 4.-
5. Quadratic Spaces of Rank 5 and 6.-
6. Hermitian Modules of Low Rank.-
7. Composition of Quadratic Spaces.- VI. Splitting and Cancellation Theorems.-
1. Semilocal Rings, the Stable Range.-
2. The f-Rank.-
3. Serre's Splitting Theorem andCancellation.-
4. Unitary Groups.-
5. Cancellation for Unitary Spaces over Semilocal Rings.-
6. Cancellation and Stability for Unitary Spaces.-
7. A Splitting Theorem.- VII. Polynomial Rings.-
1. Principal Ideal Domains.-
2. Polynomial Rings.-
3. Bundles over $$mathbb{P}^1_D$$.-
4. The Theorem of Karoubi.-
5. Quillen's Theorem.-
6. A Rigidity Theorem and the Horrocks Theorem.-
7. Isotropic Hermitian Spaces.-
8. Projective Modules over Polynomial Rings.-
9. Hermitian Spaces of Low Rank.-
10. Indecomposable Anisotropic Spaces.-
11. Hermitian Modules over Projective Spaces.- VIII. Witt Groups of Affine Rings.-
1. Witt Group of Schemes.-
2. Domains of Dimension ?3.-
3. Regular Local Rings Essentially of Finite Type.-
4. Real Smooth Surfaces.-
5. Real Curves.-
6. Examples.-
7. Symplectic Bundles over Affine Surfaces.