TITLE: Understanding singularities of differential equations
QUESTION [5 upvotes]: Is there a simple reference which explains how to see geometrically an algebraic differential equation ?
I tried to read "Équation différentielles à points singuliers réguliers" of Pierre Deligne but it was a bit too complicated for me. 
I only follow a basic course on Riemann surfaces, is there some reference or books which can helps me to understand it better this paper of Deligne (or more generally what is the geometry hidden behind theses equations and these singularities ?
Thanks in advance and sorry if my question is a bit unclear.

REPLY [3 votes]: According to this the theory of linear differential equations has been generalized to the geometry of connections on manifolds, and the monodromy of their solutions in terms of representations of fundamental groups (note the theory of special functions arising from linear differential equations is unified via representation theory). Naturally it should be possible to analyze all of this with stokes theorem or more generally cohomology and sheaves, thus as this (following Deligne) shows one should be able to unify all these interpretations to discuss singularities, and relate it all to Riemann-Hilbert problems. 
I think one can view this as the inverse Piccard-Vessiot problem, with the direct problem being treated in an introductory way in Abel's theorem & Galois' Dream.