The goal of these four lectures is to explain to the listener with no prior knowledge of mathematical logic enough of the key concepts of model theory to understand the definition and the power of the notion of o-minimality.

Lectures 1 and 2: language, structure, definable sets, elementary equivalence, model completeness and quantifier elimination, geometric interpretation, Hilbert's 17th problem, techniques for proving quantifier elimination

Lecture 3 and 4: Examples of proving model completeness/ quantifier elimination: real closed fields; the real field with restricted analytic functions; the real field with a predicate for integer powers of 2.