Abstarct: The relativistic mean field (RMF) theory has been successful in explanation of nuclear phenomena related to unstable nuclei as well as stable nuclei. Compared with non-relativistic mean field theory, relativistic mean field theory can reproduce the real characteristics of nuclear saturation in nuclear matter, and therefore provide the spin-orbit coupling potential. In this thesis, the relativistic mean field theory was employed through the shell and cluster models in order to calculate the group energy levels of weakly-bound nuclei..........