Treballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2018, Director: Albert Mas Blesa[en] This work revolves on Navier-Stokes equations. In a first part, we investigate the conservation laws of mass and momentum in order to deduce the partial differential equations that governs Newtonian fluids dynamics. The distinction between a com- pressible/incompressible fluid is treated and some elementary examples, such as the ideal fluids, are also considered. In a second part we apply numerical methods to solve some 2-dimensional problems on partial differential equations, starting from a simple one on the heat equation and finishing with one on Navier-Stokes equations.