1. Model Theory on Finite Structures. In this lecture I will discuss what model theoretic methods are available when only finite structures are considered. I will show how the classical compactness and completeness theorems fail, and illustrate the use of Ehrenfeucht-Fraïsse; games. I will also present a proof of the 0-1 law for first order logic.

2. Logical Characterisations of Complexity. I will present results on the characterisation of computational complexity classes as definability classes in various logics. This includes the theorems of Fagin, Immerman and Vardi. The focus will be on the role played by a linear order in these results. I will discuss how some complexity theoretic questions can be characterised without the assumption of an order, and the significance of such results.

3. Finite Models and Circuit Complexity. In the final lecture of the series, I will discuss relationships between the logical characterisations obtained in finite model theory and circuit complexity.