Euclid is an astronomical spacecraft project set up by a European consortium and selected by the European Space Agency (ESA) in 2011 as a medium class mission of the Cosmic Vision 2015-2025 program. Recent astronomical observations indicate that our Universe is dominated by dark matter and energy of a so-far unknown nature. The Euclid plan is to survey almost all of the extragalactic sky, with a mosaic of sharp images and spectra for the relatively bright sources. The main goal is to infer the amount and the distribution of these obscure and mysterious matter / energy from the detailed properties of the distant light-emitting galaxies. This will be a major step forwards for a better understanding of the structure and of the history of our Universe.