Papers resulting from a course held at the University of California at Berkeley, 199091 and the AMS Special Session on Real Algebraic Geometry and Quadratic Forms held in San Francisco, Jan. 1991, both comprising the special year dubbed RAGSQUAD.

Includes bibliographical references.

D. W. Dubois and the pioneer days of real algebraic geometry ; On algebraic structures of manifolds ; On local uniformization of orderings ; Real algebraic geometry over eal closed fields ; On the reduction of semialgebraic sets by real valuations ; Orderings for noncommutative rings ; Nonexistence of analytically varying solutions to Hilbert's 17th problem ; A combinatorial geometric structure on the space of orders of a field. II ; Formal determination of polynomial consequences of real orthogonal matrices ; On valuation spectra ; Minimal generation of basic sets in the real spectrum of a commutative ring ; A new proof of the homogeneous Nullstellensatz for ields, and applications to topology ; The compatible valuation rings of the coordinate ring of the real plane ; Estimates for parametric nonuniformity in representations of a definite polynomial as a sum of fourth powers ; On generators for the Witt ring ; On the trace formula for quadratic forms ; Quadratic forms with values in line bundles ; On annihilators in graded Witt rings and in Milnor's heory ; An application of the theory of order completions ; Growth of the nvariant under algebraic extensions ; Remarks on Merkurjev's investigations of the nvariant ; On the canonical class of a curve and the extension property for quadratic forms ; Reduced norms and Pfaffians via BrauerSeveri schemes ; Matching Witts with global fields ; On Wittkernels of function fields of curves ; On the canonical class of hyperelliptic curves Tomas Recio and Carlos Andradas ; S Akbulut ; Carlos Andradas and Jesus M Ruiz ; Ralph Berr ; Ludwig Brocker ; Thomas C Craven ; Charles N Delzell ; M A Dickmann ; M J GonzalezLopez and T Recio ; Roland Huber and Manfred Knebusch ; M Marshall ; Albrecht Pfister ; M J de la Puente ; Gilbert Stengle ; Jon Kr Arason Richard Elman and Bill Jacob ; Eberhard Becker and Thorsten Woermann ; W Bichsel and MA Knus ; Martin Kruskemper ; Ka Hin Leung ; David B Leep and A S Merkurjev ; Jan Minac ; R Parimala and W Scharlau ; R Parimala and R Sridharan ; R Perlis K Szymiczek P E Conner and R Litherland ; Jonathan Shick ; V Suresh