This is the first of several meetings in which we will go through Ehud Hrushovski´s paper "Computing the Galois group of a linear differential equation". This paper can be viewed as obtaining an analog of the Bertini- Noether theorem (as in the book Field Arithmetic) but for linear differential equations instead of for polynomial equations. The paper uses ideas from model theory and algebraic geometry. Participants are encouraged to look at the paper beforehand. At least in this initial meeting, we will not follow the traditional lecture format.