From my first analysis course to my M2, I was certain that differential equations were not my cup of tea.

Well, all this time I have been wrong and I will tell you how I learned to love them.

In this talk I will present you (through some particular cases and an important exemple) the 21st Hilbert problem, about complex differential systems of Fuchsian type and their monodromy data, and the history of a century of its (non-)solution. In the end, I will introduce the definition of logarithmic connection on a vector bundle an we will see how it leads to a result even more deep and beautiful than Hilbert 21st. It is the so called Riemann-Hilbert correspondance.