I: Basic facts about symmetric bilinear forms, and definition of the Wittring..- § 1 Bilinear Spaces.- § 2 Witt- and Grothendieck-rings.- Appendix: Quadratic Forms.- II: The structure of Wittrings.- § 1 Generators and Relations.- § 2 The prime ideals of a Wittring.- § 3 Nilpotent and torsion elements.- § 4 Application: The theorem of Artin-Pfister.- § 5 Complements to the structure theory.- § 6 Characterization of abstract Wittrings.- § 7 Fields with isomorphic Wittrings.- III: Reduced Wittrings.- § 1 Von Neumann regular rings.- § 2 Topological description of reduced Wittrings.- § 3 A Nullstellensatz for Witt ideals and a generalization of the theorem of Artin-Pfister.- § 4 When are Wittrings group rings?.- § 5 Fields with strong approximation for orderings.- References.
