This volume has grown out of lectures given by Professor Pfister
over many years. The emphasis here is placed on results about
quadratic forms that give rise to interconnections between number
theory, algebra, algebraic geometry and topology. Topics discussed
include Hilbert's 17th problem, the Tsen-Lang theory of quasi
algebraically closed fields, the level of topological spaces and
systems of quadratic forms over arbitrary fields. Whenever possible
proofs are short and elegant, and the author's aim was to make this
book as self-contained as possible. This is a gem of a book
bringing together thirty years' worth of results that are certain
to interest anyone whose research touches on quadratic forms.
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