Treballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2016, Director: Carles SimóDifferential Galois Theory opens the door to a fairly recent field of study. Revisiting the ideas behind Galois theory of algebraic equations in polynomials, we will learn on the development of an analogous approach applied to differential equations. We will provide links with Dynamical Systems in terms of integrability, in particular, of Hamiltonian Systems. Finally, we will apply our results to a particular example and design our own original strategy to apply the theory.