Absolute values and their completions -like the p-adic number
fields- play an important role in number theory. Krull's
generalization of absolute values to valuations made applications
in other branches of mathematics, such as algebraic geometry,
possible. In valuation theory, the notion of a completion has to be
replaced by that of the so-called Henselization.
In this book, the theory of valuations as well as of
Henselizations is developed. The presentation is based on the
knowledge acquired in a standard graduate course in algebra. The
last chapter presents three applications of the general theory -for
instance to Artin's Conjecture on the p-adic number fields- that
could not be obtained by the use of absolute values alone.
General
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