In this work we have made a revision of classical methods for dimensionality reduction and clustering. After seen the disadvantages of these approaches, we conclude that the main problem is that they do not consider the explicit form of the differential manifold structure in which our data probably lie. With the purpose of solving this problem we have focused this work in the study of advanced methods for dimensionality reduction and clustering, specifically Laplacian Eigenmaps (LE) and Spectral Clustering algorithms. The main advantages of these techniques is that they reduced the dimension of our original data, preserving the local geometric information of the points. The embedding of the points corresponds with the subjacent manifold to which the original data belongs.