Treballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2017, Director: Núria Fagella Rabionet[en] Riemann theorem and its applications in the complex dynamic systems are studied in this final degree project. In this work we will prove that the complementary of Julia set together with the complementary of Mandelbrot set are conformally equivalent with the external of the unitary disc. Although the boundary of these sets is highly fractal, using the function dynamics, we are going to express practically in an explicit way the Riemann conformal map.