Wittrings

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.