ESPRESSO is the next generation ground based European exoplanets hunter. It will combine the efficiency of modern echelle spectrograph with extreme radial-velocity and spectroscopic precision. It will be installed at Paranal's VLT in order to achieve two magnitudes gain with respect to its predecessor HARPS, and the instrumental radial-velocity precision will be improved to reach 10 cm/s level. We have constituted a Consortium of astronomical research institutes to fund, design and build ESPRESSO on behalf of and in collaboration with ESO, the European Southern Observatory. The spectrograph will be installed at the Combined Coudé Laboratory (CCL) of the VLT, it will be linked to the four 8.2 meters Unit Telescopes through four optical "Coudé trains" and will be operated either with a single telescope or with up to four UTs, enabling an additional 1.5 magnitude gain. Thanks to its characteristics and ability of combining incoherently the light of 4 large telescopes, ESPRESSO will offer new possibilities in many fields of astronomy. Our main scientific objectives are, however, the search and characterization of rocky exoplanets in the habitable zone of quiet, near-by G to M-dwarfs, and the analysis of the variability of fundamental physical constants. The project is, for most of its workpackages, in the procurement or development phases, and the CCL infrastructure is presently under adaptation work. In this paper, we present the scientific objectives, the capabilities of ESPRESSO, the technical solutions for the system and its subsystems. The project aspects of this facility are also described, from the consortium and partnership structure to the planning phases and milestones.