The role of Euclid in cosmology (and much more) \ldots\ .

Euclid was selected in the framework of the ESA Cosmic Vision 2015--2025 as a M-class mission and will be launched in 2023 (TBC). Euclid is a cosmological survey mission based on a $1.2 {m}$ diameter telescope. It will cover $15000 {deg^{2}}$ (Wide Survey) with visible (broad-band red filter) plus near-infrared imaging (Y, J, H filters), and with near-infrared spectroscopy in the $1.25\mbox{--}1.85 {micron}$ spectral range. In addition, the Deep Survey will observe in imaging (optical and near-infrared) $40 {deg^{2}}$ going deeper by 2 magnitudes than the Wide Survey, and additional spectroscopy will also be done at $0.92\mbox{--}1.35 {micron}$ for further studies on galaxy formation and evolution. Euclid will provide high-quality images and optical/near-IR photometry for more than 2 billion galaxies, as well as redshifts and spectra for tens of million galaxies out to redshift around 2 and beyond. The revolutionary power of Euclid relies on the combination of different, independent and complementary probes capable to address the key questions of cosmology (dark energy, modified gravity, relations between luminous and dark matter): weak gravitational lensing, baryonic acoustic oscillations, redshift-space distorsions, galaxy clusters, and cross-correlations with the CMB (Laureijs $et al.$, 2011). The legacy value of the Euclid dataset will be immense for a wide range of science cases. In particular, Euclid will place tight constraints on galaxy formation and evolution with unprecedented statistics. Last but not least, the Deep Survey will allow us to shed light on the first phases of galaxy and massive black-hole formation in the young Universe during the first billion years after the Big Bang. The contribution will focus on the scientific role of Euclid, the synergies with other facilities in the next decade, and the growth of the Italian community thanks to this space mission.