Euclid is a Medium Class mission of the ESA Cosmic Vision 2015-2025 programme, designed to map the geometry of the dark Universe. It is a space mission that will study the expansion history of the Universe and the distribution of dark matter and dark energy. The mission will use two primary cosmological probes: Weak gravitational Lensing (WL) and Baryonic Acoustic Oscillations (BAO). WL will measure the distribution of dark matter by quantifying the apparent distortions of galaxy images, while BAO will use wiggle patterns in the clustering of galaxies to measure the expansion of the Universe. The mission will also study the nature of dark energy and gravity by tracking their observational signatures on the geometry of the universe and on the cosmic history of structure formation. The Euclid mission will be launched in 2018 on a Soyuz ST-2.1B rocket, with an all-year round launch window. It will map large-scale structure over a cosmic time covering the last 10 billion years, more than 75% the age of the Universe. The mission is optimised for two independent primary cosmological probes: WL and BAO. The mission will use a 1.2 m Korsch telescope to provide a large field of view. The telescope directs the light to two instruments via a dichroic filter in the exit pupil. The reflected light is led to the visual instrument (VIS) and the transmitted light from the dichroic feeds the near infrared instrument (NISP) which contains a slitless spectrometer and a three bands photometer. Both instruments cover a large common field-of-view of ~0.54 deg². The VIS is equipped with 36 CCDs. It measures the shapes of galaxies with a resolution better than 0.2 arcsec (PSF FWHM) with 0.1 arcsec pixels in one wide visible band (R+I+Z). The NISP photometer contains three NIR bands (Y, J, H), employing 16 HgCdTe NIR detectors with 0.3 arcsec pixels. The spectroscopic channel of NISP operates in the wavelength range 1.1-2.0 micron at a mean spectral resolution λ/Δλ~250, employing 0.3 arcsec pixels. While the VIS and NISP operate in parallel, the NISP performs the spectroscopy and photometry measurements in sequence by selecting a grism wheel in case of spectroscopy and a filter wheel in case of photometry. The mission will be launched in 2018 on a Soyuz ST-2.1B rocket, with an all-year round launch window. A direct transfer of ~30 days is targeted to a large-amplitude free-insertion orbit at the 2nd Lagrange Point of the Sun-Earth System. It takes 6 years to complete a wideEuclid is a Medium Class mission of the ESA Cosmic Vision 2015-2025 programme, designed to map the geometry of the dark Universe. It is a space mission that will study the expansion history of the Universe and the distribution of dark matter and dark energy. The mission will use two primary cosmological probes: Weak gravitational Lensing (WL) and Baryonic Acoustic Oscillations (BAO). WL will measure the distribution of dark matter by quantifying the apparent distortions of galaxy images, while BAO will use wiggle patterns in the clustering of galaxies to measure the expansion of the Universe. The mission will also study the nature of dark energy and gravity by tracking their observational signatures on the geometry of the universe and on the cosmic history of structure formation. The Euclid mission will be launched in 2018 on a Soyuz ST-2.1B rocket, with an all-year round launch window. It will map large-scale structure over a cosmic time covering the last 10 billion years, more than 75% the age of the Universe. The mission is optimised for two independent primary cosmological probes: WL and BAO. The mission will use a 1.2 m Korsch telescope to provide a large field of view. The telescope directs the light to two instruments via a dichroic filter in the exit pupil. The reflected light is led to the visual instrument (VIS) and the transmitted light from the dichroic feeds the near infrared instrument (NISP) which contains a slitless spectrometer and a three bands photometer. Both instruments cover a large common field-of-view of ~0.54 deg². The VIS is equipped with 36 CCDs. It measures the shapes of galaxies with a resolution better than 0.2 arcsec (PSF FWHM) with 0.1 arcsec pixels in one wide visible band (R+I+Z). The NISP photometer contains three NIR bands (Y, J, H), employing 16 HgCdTe NIR detectors with 0.3 arcsec pixels. The spectroscopic channel of NISP operates in the wavelength range 1.1-2.0 micron at a mean spectral resolution λ/Δλ~250, employing 0.3 arcsec pixels. While the VIS and NISP operate in parallel, the NISP performs the spectroscopy and photometry measurements in sequence by selecting a grism wheel in case of spectroscopy and a filter wheel in case of photometry. The mission will be launched in 2018 on a Soyuz ST-2.1B rocket, with an all-year round launch window. A direct transfer of ~30 days is targeted to a large-amplitude free-insertion orbit at the 2nd Lagrange Point of the Sun-Earth System. It takes 6 years to complete a wide