Treballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2017, Director: Teresa Crespo Vicente[en] The goal of this project is to classify the real forms of a closed subgroup of the special linear complex group of degree two. Previously we have to study several concepts of algebraic group theory such as galois cohomology. We expose many properties of forms of an algebraic group over a field $k$. We present the Kovacic algorithm for solving second order linear homogeneous differential equation over $\mathbb{C}(x)$.