Positivity is one of the most basic mathematical concepts. In many
areas of mathematics (like analysis, real algebraic geometry,
functional analysis, etc.) it shows up as positivity of a
polynomial on a certain subset of R DEGREESn which itself is often
given by polynomial inequalities. The main objective of the book is
to give useful characterizations of such polynomials. It takes as
starting point Hilbert's 17th Problem from 1900 and explains how E.
Artin's solution of that problem eventually led to the development
of real algebra towards the end of the 20th century. Beyond basic
knowledge in algebra, only valuation theory as explained in the
appendix is needed. Thus the monograph can also serve as the basis
for a 2-semester course in real a
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