A Stochastic Differential Equation is roughly an ordinary Differential Equation with an additional perturbation, that is a random noise. As a consequence, its solutions are time-indexed random variables. A crucial problem is whether or not these random variables admit a density with respect to Lebesgue’s measure. This question was partially solved by Hormander and Malliavin and is still an active research field. Malliavin’s proof was also the birth act of Malliavin Calculus, which is basically a complete Integro-Differential theory for stochastic processes. After introducing the notions related to Stochastic Integral Calculus and Stochastic Differential Equations, I will discuss the basic notions of Malliavin Calculus, which are the relevant tools to address this problem. I will then finish by sketching the proof of Hormander’s Theorem.