The melting of crystal phases in two-dimensional systems has been the subject of a large amount of theoretical, numerical and experimental works. Several mechanisms to describe the melting in two dimensions were proposed, e.g., the KTHNY theory and the melting induced by formation of grains boundaries. There are strong evidence that the melting in two dimensions depends crucially on the form and range of the interaction potentials between particles. We report extensive Monte Carlo studies of the melting of the classical two-dimensional crystal for systems of point particles interacting via the potential for and 3; the long ranged interaction is taken into account with the Ewald method. In this contribution, we focus on the statistical analysis of topological defects and of the unbinding transitions of the dislocations and disclinations pairs which permits to obtain a better description of the two-dimensional melting.