Treballs finals del Màster en Matemàtica Avançada, Facultat de matemàtiques, Universitat de Barcelona, Any: 2016, Director: Marta Sanz[en] This master thesis gives an extensive introduction to the Rough Path Analysis theory presented by Terry Lyons in the late 90’s, which provides a pathwise approach to stochastic calculus. The most important result of this mathematical theory states the continuity of the Itô map with respect to a general control if we move to a new framework where the notion of path is substituted by these more involved objects: the rough paths, and the metric also becomes more complex.