Introduction To Quadratic Forms Over Fields
T. Y. Lam
Amer Mathematical Society
This new version of the author's prizewinning book, Algebraic  Theory of Quadratic Forms (W. A. Benjamin, Inc., 1973), gives a  modern and self-contained introduction to the theory of  quadratic forms over fields of characteristic different from  two. Starting with few prerequisites beyond linear algebra, the  author charts an expert course from Witt's classical theory of  quadratic forms, quaternion and Clifford algebras,  Artin-Schreier theory of formally real fields, and structural  theorems on Witt rings, to the theory of Pfister forms, function  fields, and field invariants. These main developments are  seamlessly interwoven with excursions into Brauer-Wall groups,  local and global fields, trace forms, Galois theory, and  elementary algebraic K-theory, to create a uniquely original  treatment of quadratic form theory over fields. Two new chapters  totaling more than 100 pages have been added to the earlier  incarnation of this book to take into account some of the newer  results and more recent viewpoints in the area. <P>As is characteristic of this author's expository style, the  presentation of the main material in this book is interspersed  with a copious number of carefully chosen examples to illustrate  the general theory. This feature, together with a rich stock of  some 280 exercises for the thirteen chapters, greatly enhances  the pedagogical value of this book, both as a graduate text and  as a reference work for researchers in algebra, number theory,  algebraic geometry, algebraic topology, and geometric topology.