Model theory and applications

Model theory is a branch of mathematical logic that deal with structures (models), historically with connections to other areas of mathematics. In this talk I plan to give the fundamental theorems of first order model theory, various examples and mention some applications to areas such as algebraic geometry and number theory (maybe some comments about the connection with motivic integration). Some words that will appear in my talk: first order languages, compactness theorem, Gödel's completeness theorem, definable sets, stability, o-minimality, Ax-Kochen principle.