Abstract : The control of Edge Localized Modes (ELMs) is a capital question for the future ITER tokamak. The present work is dedicated to one of the most promising methods of control of the ELMs, based on a system of coils producing Resonant Magnetic Perturbations (RMPs! ), the efficiency of which was first demonstrated in the DIII-D tokamak in 2003. Our main objectives are, on the one hand, to improve the physical understanding of the mechanisms at play, and on the other hand to propose a concrete design of ELMs control coils for ITER. In order to calculate and analyze the magnetic perturbations produced by a given set of coils, we have developed the ERGOS code. The first ERGOS calculation was for the DIII-D ELMs control coils, the I-coils. It showed that they produce magnetic islands chains which overlap at the edge of the plasma, resulting in the ergodization of the magnetic field. We have then used ERGOS for the modelling of the experiments on ELMs control using the error field correction coils at JET and MAST, to which we participate since 2006. In the case of JET, we have shown the existence of a correlation between the mitigation of the ELMs and the ergodization of the magnetic field at the edge, in agreement with the DIII-D result. The design of ELMs control coils for ITER was done principally in the frame of an EFDA (European Fusion Development Agreement)-CEA contract, in collaboration with engineers from EFDA and ITER. We used ERGOS intensitvely, taking the case of the DIII-D I-coils as a reference. Three candidate designs came out, which we presented at the ITER Design Review, in 2007. Recently, the ITER management decided to provide a budget for building ELMs control coils, the design of which remains to be chosen between two of the three options that we proposed (or close to the ones we proposed). Finally, in order to understand better the non-linear magnetohydrodynamics phenomena taking place in ELMs control by RMPs, we performed numerical simulations, in particular with the JOREK code for a DIII-D case. The simulations reveal the existence of convection cells induced at the edge by the magnetic perturbations, and the possible screening of the RMPs in presence of rotation. The adequate modelling of the screening, which requires to add more physics into JOREK, has been started.