Abstract : One of the main goals of classical and quantum physics is to solve the many-body problem. In nuclear theory, several methods have been developed and provide accurate results. In this thesis, we remind how symmetry can be used to obtain analytical solutions of the quantum many-body problem. We emphasize that unitary Lie algebras play a crucial role in quantum mechanics and propose and implement a method to build irreducible representations of this algebra from its highest-weight state. Calculations of bosonic and fermionic spectra are performed with realistic and with random interactions. Studies with rotationnal invariant two-body random interactions have unveiled high degree of order (e.g. a marked statistical preference is found for ground states with angular momentum equal to zero). In the second chapter of this thesis, it is argued that the spectral properties of this kind of interaction depend on the choice of the valence space. In particular, we propose a geometrical method to predict the properties of the ground state in certain cases. We also present numerical results when the geometrical approach can not be applied. In the third chapter, we study the link between quantum chaos and nuclear spectra calculated with realistic interactions.