The aim of this paper is to introduce the WIRCam Ultra Deep Survey (WUDS), a near-IR photometric public survey carried out at the CFH Telescope in the field of the CFHTLS-D3 field (Groth Strip). WUDS includes four near-IR bands (Y, J, H and K_s) over a field of view of ~400 arcmin^2. The typical depth of WUDS data reaches between ~26.8 in Y and J, and ~26 in H and K_s (AB, 3 sigma in 1.3 arcsec aperture). The area and depth of this survey were specifically tailored to set strong constraints on the cosmic star formation rate and the luminosity function brighter or around L* in the z~6-10 redshift domain, although these data are also useful for a variety of extragalactic projects.This first paper is intended to present the properties of WUDS: catalog building, completeness and depth, number counts, photometric redshifts, and global properties of the galaxy population. We have also concentrated on the study of galaxy samples at z~[4.5-7] in this field. UV luminosity functions were derived at z~5 and z~6 taking advantage from the fact that WUDS covers a particularly interesting regime at intermediate luminosities, which allows a combined determination of M* and Phi* with increased accuracy. Our results on the luminosity function are consistent with a small evolution of both M* and Phi* between z=5 and z=6, irrespective of the method used to derive them, either photometric redshifts applied to blindly-selected dropout samples or the classical Lyman Break Galaxy color-preselected samples. Our results lend support to higher Phi* determinations at z=6 than usually reported. The selection and combined analysis of different galaxy samples at z>7 will be presented in a forthcoming paper. WUDS is intended to provide a robust database in the near-IR for the selection of targets for detailed spectroscopic studies, in particular for the EMIR/GTC GOYA Survey (Abridged)
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