The purpose of this course is to learn the fundamental results about the model theory of difference fields, as developed in Chatzidakis and Hrushovski [10]. The goal is to get to a level that will allow reading that paper. In this section we give some basic definitions, and mention some of the applications of this theory. A more detailed description of the content of the course can be found in ...

are given, u1 and u11 are defined according to the partition of A, i.e. u1 = (wU), • • -, um)', ulL = (w<!+1), • • -, uM)', and *S is a given constant rectangular matrix. It is well known that the above problem is correctly posed in L2 (see for example Thomée [4]). The present treatment of the case when A is a constant matrix can be extended, as in [1], to the case when A depends on (x, t) in a...