Papers resulting from a course held at the University of California at Berkeley, 1990-91 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 / Tomás Recio & Carlos Andradas -- On albegraic structures of manifolds / S. Akbulut -- On local uniformization of orderings / Carlos Andradas and Jesús M. Ruiz -- Real algebraic geometry over p-real closed fields / Ralph Berr -- On the reduction of semialgebraic sets by real valuations / Ludwig Bröcker -- Orderings for noncommutative rings / Thomas C. Craven -- Nonexistence of analytically varying solutions to Hilbert's 17th problem / Charles N. Delzell -- A combinatorial geometric structure on the space of orders of a field II / M.A. Dickmann -- Formal determination of polynomial consequences of real orthogonal matrices / M.J. González-Lopez and T. Recio -- On valuation spectra / Roland Huber and Manfred Knebusch -- Minimal generation of basic sets in the real spectrum of a commutative ring / M. Marshall -- A new proof of the homogeneous nullstellensatz for p-fields and applications to topology / Albrecht Pfister -- The compatible valuation rings of the coordinate ring of the real plane / M.J. de la Puente -- Estimates for parametric nonuniformity in representations of a definite polynomial as a sum of fourth powers / Gilbert Stengle -- On generators for the Witt ring / Jón Kr. Arason, Richard Elman, and Bill Jacob -- On the trace formula for quadratic forms / Eberhard Becker and Thorsten Wöermann -- Quadratic forms with values in line bundles / W. Bichsel and M.-A. Knus -- On annhilators in graded Witt rings and in Milnor's K theory / Martin Krüskemper -- An application of the theory of order completions / Ka Hin Leung -- Growth of the u-invariant under algebraic extensions / David B. Leep and A.S. Merkurjev -- Remarks on Merkurjev's investigations of the u-invariant / Ján Miná#c -- On the canonical class of a curve and the extension property for quadratic forms / R. Parimala and W. Scharlau -- Reduced norms and Pfaffians via Brauer-Severi schemes / R. Parimala and R. Sridharan -- Matching Witts with global fields / R. Perlis ... [et al.] -- On Witt-kernels of function fields of curves / Jonathan Shick -- On the canonical class of hyperelliptic curves / V. Suresh .