The book deals with the (elementary and introductory) theory of valuation rings. As explained
in the introduction this represents a useful and important viewpoint in algebraic geometry
especially concerning the theory of algebraic curves and their function fields. The
correspondences of this with other viewpoints (e.g. of geometrical or topological nature) are
often indicated also to provide motivations and intuition for many results. Links with
arithmetic are also often indicated. There are three appendices concerning Hilbert's
Nullstellensatz (for which several proofs are provided) Puiseux series and Dedekind domains.
There are also several exercises often accompanied by hints which sometimes develop further
results not included in full for brevity reasons.
