  Euclid is a European Space Agency medium class mission selected for launch in
2019 within the Cosmic Vision 2015-2025 programme. The main goal of Euclid is
to understand the origin of the accelerated expansion of the Universe. Euclid
will explore the expansion history of the Universe and the evolution of cosmic
structures by measuring shapes and redshifts of galaxies as well as the
distribution of clusters of galaxies over a large fraction of the sky. Although
the main driver for Euclid is the nature of dark energy, Euclid science covers
a vast range of topics, from cosmology to galaxy evolution to planetary
research. In this review we focus on cosmology and fundamental physics, with a
strong emphasis on science beyond the current standard models. We discuss five
broad topics: dark energy and modified gravity, dark matter, initial
conditions, basic assumptions and questions of methodology in the data
analysis. This review has been planned and carried out within Euclid's Theory
Working Group and is meant to provide a guide to the scientific themes that
will underlie the activity of the group during the preparation of the Euclid
mission.
