Interactions between model theory and algebra, especially algebraic
geometry, began in late 40's early 50's with Tarski's theorem on
quantifier elimination for theory of algebraically closed fields. These
interactions developed over the time and today they are hard tooverestimate, as they constitute the hard core of many deep theorems.
I will introduce basic model theoretic notions and present some classical applications to algebra; the idea here is to provide a qualitatively new view of old and well-known material. The talk does not assume any
knowldedge on model theory. All applications I present use tools that were known long before the development of modern model theory.