An introduction to valued fields

Abstract

The aim of this chapter is to give a short introduction to the algebra of valued fields and thereby to provide the necessary background for the following two chapters. The material presented here is heavily based on the book "Valued Fields" by Engler and Prestel, as well as (unpublished) lectures given by Jochen Koenigsmann at the University of Oxford in Hilary 2010. Many of the proofs presented are taken from (or at least inspired by) one of these two sources.