Model theory of valued fields

A valued field is an algebraic object that plays a role analogous to that of a ``small disc around 0’’ in geometry. In this course we will focus on the model theory of such fields, and its uses. The course will begin with a review of basic results on the first order theory of algebraically closed valued fields, such as quantifier elimination and structure of sets definable in one variable. We will the discuss elimination of imaginaries, integration theory, stable domination and the structure of the type space, and the analogy with Berkovich spaces.