Introduction
Part 1: Classical theory of symmetric bilinear forms and quadratic forms
Chapter 1. Bilinear forms
Chapter 2. Quadratic forms
Chapter 3. Forms over rational function fields
Chapter 4. Function fields of quadrics
Chapter 5. Bilinear and quadratic forms and algebraic extensions
Chapter 6. u-invariants
Chapter 7. Applications of the Milnor conjecture
Chapter 8. On the norm residue homomorphism of degree two

Part 2: Algebraic cycles
Chapter 9. Homology and cohomology
Chapter 10. Chow groups
Chapter 11. Steenrod operations
Chapter 12. Category of Chow motives

Part 3: Quadratic forms and algebraic cycles
Chapter 13. Cycles on powers of quadrics
Chapter 14. The Izhboldin dimension
Chapter 15. Application of Steenrod operations
Chapter 16. The variety of maximal totally isotropic subspaces
Chapter 17. Motives of quadrics

This book is a comprehensive study of the algebraic theory of quadratic forms, from classical theory to recent developments, including results and proofs that have never been published. The book is written from the viewpoint of algebraic geometry and includes the theory of quadratic forms over fields of characteristic two, with proofs that are characteristic independent whenever possible. For some results both classical and geometric proofs are given. --- summary provided by publisher