Abstract : For more than 30 years, networks of detectors on the ground have observed ten cosmic rays of probably extragalactic origin, whose energies exceed $10^20 eV$. The Pierre AUGER Observatory, currently in construction in Argentina, was especially designed to clear up the mystery of their origin. The first part of this thesis describes physical problems and the techniques of detection used. Next comes the calibration part. It is approched through : - The development of a new method to survey the water level ; - The setting up of an experiment to measure the surface detector response to electrons of a few MeV. Then, finally, 3 chapters are devoted to expose new methods of analyses aiming at determining the composition of the primary cosmic rays and at studying the physical phenomena which take place in the development of the showers in the atmosphere.