Let $K$ be a differential field with an algebraically closed field of constants $C$ of characteristic $0$. To a linear differential equation of order $n$ over $K$ one associates a differential Galois group which is an algebraic subgroup of ${\rm GL}(n,C)$. The inverse problem reads : “which linear algebraic groups occur as differential Galois group ?” The inverse problem is solved by J.-P. Ramis for local and global analytic situations. A constructive solution of the inverse problem for the differential field $C(x)$ (for connected groups) has been given by C. Mitschi and M.F. Singer.