The study of polynomial equations by Évariste Galois gave birth to Galois theory. The resolution of the polynomial equations of degree at most 4 is known since the 16th century. The approaches used (changes of variables, substitutions) had not permitted to solve equations of higher degree. After two centuries, progress was made possible thanks to the introduction of new ideas and notions, in particular, the introduction of the Galois group. Firstly, I will show how this leads to a criterion of resolubility by radicals for polynomial equations. Then, I will explain how these ideas were transposed to the study of solutions of linear differential equations. What information can a differential Galois group provide ? What is the structure of this group ? We will do a detour through analysis, and explore the concept of monodromy, to construct elements of this group. In summary, it will be a little walk from classical Galois theory to differential Galois theory, passing through algebra and analysis, to show you a small part of this broad theory.