Appears in collection : Thomas Dreyfus: Difference Galois theory

To a linear fuinctional equation, we may associate a group, that measures the algebraic relations between the solutions of the equation. In this course we will see the basic definition and how in some case it is possible compute the Galois group and recover the relations. We finish by a galoisian proof of Hölder theorem on the differential transcendance of the Gamma function (that is it satisfies no non trivial algebraic differential equations).