Reconstructing the 3D information of a scene is a common task in Computer Vision. Stereo matching is one of the most investigated techniques used to perform this task, which basically consists of, given two images of a scene seen from different view points, determining corresponding pixels in these two images and store this information in a disparity map. Several methods have been proposed to solve the stereo problem keeping good performance and giving good quality results. This is however a very arduos task which hardly achieves precise results with low computational power. In this context, the Graph Cuts method has been very much considered, which aims to solve the energy minimization problem in polinomial time. In this case the stereo problem can be modelled as an energy minimization problem and, thus solved using the Graph Cuts technique. In this work we investigate the most recent and efficient Graph Cuts methods and propose a method for establishing the correspondences between two images in the context of multi-resolution, in which a Gaussian pyramid for the input images is built and the Graph Cuts methods is applied in coarser levels, optimizing the performance and getting more precise results through the use of the alfa-expansion algorithm. The Graph Cuts and multi-resolution techniques are reviewed and the results of the proposed method are presented and evaluated compared to similar methods.