This volume of invited works collects the most recent research and developments in quadratic forms, linear algebraic groups, and cohomology; topics that are each at the intersection of algebra, number theory and algebraic geometry. The contributions to this volume are the work of renowned experts and present new results related to the research of Raman Parimala, to whom this collection is dedicated. Some specific topics presented in this volume include, Iwasawa theory, Witt groups and sheafs, Chow motives, quaternion algebras, p-adic curves, and progress on the Kato conjecture as well as topics of recent interest such as field patching and a proof of the Serre's Conjecture II for function fields of complex surfaces. This volume is intended for researchers and graduate students specializing in algebra, number theory, and algebraic geometry and may be suitable for supplementary use in an advanced graduate course.

Résumé
We dedicate this volume to Professor Parimala on the occasion of her 60th birthday. It contains a variety of papers related to the themes of her research. Parimalas rst striking result was a counterexample to a quadratic analogue of Serres conjecture (Bulletin of the American Mathematical Society, 1976). Her in uence has cont- ued through her tenure at the Tata Institute of Fundamental Research in Mumbai (19762006),and now her time at Emory University in Atlanta (2005present). A conference was held from 30 December 2008 to 4 January 2009, at the U- versity of Hyderabad, India, to celebrate Parimalas 60th birthday (see the conf- ences Web site at http://mathstat.uohyd.ernet.in/conf/quadforms2008). The or- nizing committee consisted of J.-L. Colliot-Thel ´ en ` e, Skip Garibaldi, R. Sujatha, and V. Suresh. The present volume is an outcome of this event. We would like to thank all the participants of the conference, the authors who have contributed to this volume, and the referees who carefully examined the s- mitted papers. We would also like to thank Springer-Verlag for readily accepting to publish the volume. In addition, the other three editors of the volume would like to place on record their deep appreciation of Skip Garibaldis untiring efforts toward the nal publication.

Contenu
Surveys.- Multiples of forms.- On Saltman's p-Adic Curves Papers.- Serre's Conjecture II: A Survey.- Field Patching, Factorization, and LocalGlobal Principles.- Deformation Theory and Rational Points on Rationally Connected Varieties.- Recent Progress on the Kato Conjecture.- Elliptic Curves and Iwasawa's µ = 0 Conjecture.- Cohomological Invariants of Central Simple Algebras with Involution.- Witt Groups of Varieties and the Purity Problem.- Invited articles.- Some Extensions and Applications of the Eisenstein Irreducibility Criterion.- On the Kernel of the Rost Invariant for E8 Modulo 3.- Une version du théorème d'Amer et Brumer pour les zéro-cycles.- Quaternion Algebras with the Same Subfields.- Lifting of Coefficients for Chow Motives of Quadrics.- Upper Motives of Outer Algebraic Groups.- Triality and étale algebras.- Remarks on Unimodular Rows.- Vector Bundles Generated by Sections and Morphisms to Grassmannians.- Adams Operations and the Brown-Gersten-Quillen Spectral Sequence.- Non-self-dual Stably Free Modules.- Homotopy Invariance of the Sheaf WNis and of Its Cohomology.- Imbedding Quasi-split Groups in Isotropic Groups.