Abstract : In this thesis, we were interested in the interplay between the spin-orbit coupling and electronic correlations in condensed matter physics. The spin-orbit interaction has indeed been found to play a significant role in the properties of a growing variety of materials, such as the topological band insulators or the iridium-based 5d-transition metal oxides. Particularly, strontium iridate (Sr2IrO4) was recently described as a "spin-orbit driven Mott insulator": according to this picture, the cooperative interaction between electronic Coulomb interactions and the spin-orbit coupling can explain the insulating state of the compound. We have studied the paramagnetic insulating phase of this material within LDA+DMFT, a method which combines the density functional theory in the local density approximation (LDA) with dynamical mean-field theory (DMFT). Sr2IrO4 was found to be a Mott insulator for a reasonable value of the electronic correlations once both the spin-orbit coupling and the lattice distortions were taken into account. Moreover, our results highlight the respective roles played by theses two features to reach the Mott insulating state and emphasize that only their acting together may open the Mott gap in such a compound. In order to perform this study, the spin-orbit interaction was included in the LDA+DMFT formalism. The interest of such a technical development goes beyond the present case of Sr2IrO4 since this "LDA+SO+DMFT implementation" could be also used to take into account the electronic correlations in the description of other 5d-transition metal oxides or even topological band insulators.