This dissertation deals with aspects of many-body problem in the electronic structure of solids. More specifically, we study how the introduction of Green’s function of many bodies and their equation of motion leads to information about the interactions between particles. Thus, we get to the GW and Bethe-Salpeter formalisms. We show in specific cases how the GW is able to describe energy gaps at a level that goes beyond the Density Functional Theory. Likewise, we investigate the inclusion of excitonic effects through the Bethe-Salpeter equation, showing how the approach can provide optical spectra in good agreement with experimental results. We exemplify the above points with the discussion of specific cases.