The term ‘dark energy’ was coined in 1998 in the aftermath of a surprising discovery. While the expansion of the Universe predicted by the Big Bang theory has been confirmed by the observation of galaxies moving away from each other, this expansion appears to be accelerating over time. This phenomenon cannot be explained by current theories, which predict that the expansion should be stable or slowing down due to the effects of gravitation. In addition, this shadowy component appears to account for 73% of the content of the Universe, together with an additional 23% made up of the equally mysterious ‘dark matter’ whose effects can be observed on a large scale. This discovery, which gained its authors a Nobel Prize in 2011, has provoked considerable interest in the wider scientific community, particularly in the fields of theoretical physics, astrophysics and cosmology. A number of experimental ideas have been put forward in an attempt to understand and explain dark energy. Euclid will follow up at least two of these, Weak Lensing (WL) and Baryonic Acoustic Oscillations (BAO). The first method measures the distortion in the images of galaxies caused by the presence of dark matter along the line of sight. By making these measurements on a number of galaxies at differing distances from the Earth, it is possible to map the dark matter in three dimensions and to study changes in this distribution as a function of time. These changes are determined by the properties of dark energy.The BAO method is based on a three-dimensional mapping of large visible structures in the Universe such as galaxies and galactic clusters. This method also compares distant, and therefore old, structures with closer and more recent features in order to deduce the precise effects of dark energy.It has been found that both dark matter and dark energy have an effect on the history of the expansion of the Universe and changes in cosmic structures, but that these effects are different. Euclid will identify and characterize these differences, enabling physicists and astrophysicists to understand the nature of dark energy and to determine the properties of dark matter. Euclid will provide an answer to the question of whether the acceleration of the expansion of the Universe is due to a new component, dark energy, or whether it is simply a manifestation of gravitational effects that current gravitational theory, in the form of general relativity, fails to predict.In order to make these measurements, Euclid will survey a large section of the sky using two highly accurate instruments located at the focus of a telescope 1.2 meters in diameter. A 576 million pixel camera will capture images of around 2000 million galaxies with a high resolution equivalent to that of the Hubble Space Telescope. An infrared spectrograph and photometer will generate a map of the large structures in the Universe and will measure the distances to the galaxies imaged by the camera. Finally, a cluster of supercomputers running specialized software will be needed to process the several million gigabytes of data received from the satellite.The scientific data provided by Euclid will constitute a unique catalog of several thousand million stars and galaxies distributed across the section of sky located in the region of the Milky Way. This will provide a window on the formation of the first galaxies, over 12 000 million years ago, and will constitute a unique and almost inexhaustible source of data for the worldwide astronomical community over the coming decades.While the mission as a whole is under the overall responsibility of the ESA, the largest ever consortium of European laboratories and institutes ever brought together for a European space mission will supply the instruments and data processing systems. This aspect of the project will be led by Yannick Mellier of the Paris Astrophysics Institute (Pierre and Marie Curie University / CNRS). The founders of the consortium include a number of French laboratories supported by the CNES who have all contributed to the in-depth studies required for the successful selection of the Euclid mission. In particular, they will be responsible for supplying the infrared spectrograph and photometer, the focal plane of the visible light camera, the overall architecture of the data processing systems, a high-performance computing center, and a wide range of software packages. The following laboratories are participating in the Euclid consortium:Astrophysics Instrumentation and Modeling (Paris Diderot University / CEA-IRFU / CNRS)Astroparticle and Cosmology Laboratory (Paris Diderot University / CNRS / CEA / Paris Observatory)Center for Particle Physics of Marseille (Aix-Marseille University / CNRS)Paris Astrophysics Institute (Pierre and Marie Curie University / CNRS)Institute of Space Astrophysics (University of Paris South / CNRS)Nuclear Physics Institute of Lyon (Claude Bernard Lyon1 University / CNRS)Research Institute in Astrophysics and Planetology (Toulouse 3 - Paul Sabatier University / CNRS)Institute of Research into the Fundamental Laws of the Universe (CEA, Saclay)Marseille Astrophysics Laboratory (Aix-Marseille University / CNRS)Lagrange Laboratory (Côte d’Azur Observatory / CNRS / Nice Sophia Antipolis University)Nuclear Physics and High Energies Laboratory (Pierre and Marie Curie University / Paris Diderot University / CNRS)Computer Center of the National Institute of Nuclear and Particle Physics (CNRS).