The recent advances in experimental nuclear physics make it possible to study nuclear systems far from the beta stability line. The discovery of new phenomena, like halos or neutron skins, requires the development of new theoretical models which enable to study these systems. The first part of this work is devoted to the development and the applications of the Shell Model Embedded in the Continuum (SMEC). This new formalism allows to take into account the correlations between the bound and scattering states of losely bound nuclei. SMEC is applied here to the study of the spectroscopy of the Mirror nuclei 8B-8Li and 17F-17O. It can also be used to calculate the cross sections of the elastic scattering, the Coulomb breakup processes and the radiative n,p capture processes. The results concerning the reactions of astrophysical interst : 18O(p, $\gamma$)17F and 7Be(p, $\gamma$)8B, are discussed in détails. This last reaction is very important because the disintegration of 8B is the main source of High energy neutrinos in the sun. The second part of this work is related to the analysis of pairing interaction for weakly bound nuclei. We have developed a new approach, based on the Hartree-Fock-Bogolyubov (HFB) theory, that allows to study the pairing correlations between bound and scattering states, both resonant and not résonant ones. The " particle-hole " potential is replaced by a model potential for which the solutions are analytically known. This method allows to analyse the effect of pairing on bound and resonant states, independently of their energy position. We have clearly demonstrated that the non-resonant continuum plays a crucial role in the loosely bound nuclei and that solving the HFB equations in the coordinate space is the only method that permits to treat this problem correctly.
