The origin of ultra-high energy cosmic rays remains an enigma of modernphysics, which the Pierre Auger Observatory, a detector with a hybriddetection mode and an unprecedented size, will try to solve. The directobservation of the sources of those particles, or of large-scale structuresin the sky associated to the sources, is one of the main goals of theobservatory. Such observations should also allow to constrain cosmic raypropagation between their sources and the Earth, which is complicated byinteractions with low-energy photon backgrounds and deflections inastrophysical magnetic fields.This thesis is made of two parts, in order to observe and modelize thesources of cosmic rays within the Auger Observatory.We begin with an extensive description of the Pierre Auger Observatory, andstudy the acceptance of its surface detector in order to build accurate skyexposure maps, an essential tool in order to study anisotropies. Then wepresent methods to search for anisotropies in the sky, and analyze thefirst two years of Auger data.After a description of the phenomena that can influence the propagation andobservation of ultra-high energy cosmic ray sources, we present numericalsimulations aiming at predicting observables such as the spectrum,anisotropies and composition measurable by Auger as a function of variousastrophysical models. We show that extragalactic magnetic fields can play acrucial role in particular if cosmic rays are partly heavy nuclei. Finally,we show that the propagation of these particles from a nearby sourcegenerates secondary fluxes of gamma-rays that could be detected by TeVgamma-ray telescopes.
