Euclid mission objective is to map the geometry of the dark Universe. The mission will investigate the distance-redshift relationship and the evolution of cosmic structures. It achieves this by measuring shapes and redshifts of galaxies and clusters of galaxies out to redshifts ~2, or equivalently to a look-back time of 10 billion years. It will therefore cover the entire period over which dark energy played a significant role in accelerating the expansion.