  The energy density of the Universe is dominated by dark energy and dark
matter, two mysterious components which pose some of the most important
questions in fundamental science today. Euclid is a high-precision survey
mission designed to answer these questions by mapping the geometry of the dark
Universe. Euclid's Visible-NIR imaging and spectroscopy of the entire
extragalactic sky will further produce extensive legacy science for various
fields of astronomy. Over the 2008-2009 period, Euclid has been the object of
an ESA Assessment Phase in which the study of the Euclid Imaging instrument was
under the responsibility of the Euclid Imaging Consortium (EIC). The EIC
Science Book presents the studies done by the EIC science working groups in the
context of this study phase. We first give a brief description of the Euclid
mission and of the imaging instrument and surveys. We then summarise the
primary and legacy science which will be achieved with the Euclid imaging
surveys, along with the simulations and data handling scheme which have been
developed to optimise the instrument and ensure its science performance.
