This document is a summary of some relevant information in the field of Computational Fluid Dynamics, done to understand a typical start point problem: The Lid - Driven Cavity Problem. The main objectives of the present work are first, to understand the basic concepts related to the Navier - Stokes equations in vorticity - stream function (V-SF) and in velocity - pressure (V-P) formulations. In addition, in the former case the resulting governing equations are solved using the over relaxation method, and in the latter they are solved applying the finite volume method on a staggered grid using the Mark and Cell (MAC) method. Results in the (V-SF) case, are analyzed for a low Reynolds number such as 20, in three different situations in which the top and bottom walls move in different ways. Results in the (V-P), are analyzed for two Reynolds numbers: 400 and 10000. Those results are validated using the literature, especifically comparing with Guia et al, 1982. A physical interpretation about variations of pressure, velocity and forces is done. In the case of working with MAC method, for time evolution four different methods were employed and compared between them. These methods are: Finite Difference Scheme, Adam - Bashforth second order, Runge - Kutta second order, and Runge - Kutta fourth order.