We describe the construction and general features of VIPERS, the VIMOS Public Extragalactic Redshift Survey. This `Large Programme has been using the ESO VLT with the aim of building a spectroscopic sample of ~100,000 galaxies with i_{AB}<22.5 and 0.5<z<1.5. The survey covers a total area of ~24 deg^2 within the CFHTLS-Wide W1 and W4 fields. VIPERS is designed to address a broad range of problems in large-scale structure and galaxy evolution, thanks to a unique combination of volume (~ 5 x 10^7 h^{-3} Mpc^3) and sampling rate (~ 40%), comparable to state-of-the-art surveys of the local Universe, together with extensive multi-band optical and near-infrared photometry. Here we present the survey design, the selection of the source catalogue and the development of the spectroscopic observations. We discuss in detail the overall selection function that results from the combination of the different constituents of the project. This includes the masks arising from the parent photometric sample and the spectroscopic instrumental footprint, together with the weights needed to account for the sampling and the success rates of the observations. Using the catalogue of 53,608 galaxy redshifts composing the forthcoming VIPERS Public Data Release 1 (PDR-1), we provide a first assessment of the quality of the spectroscopic data. Benefiting from the combination of size and detailed sampling of this dataset, we conclude by presenting a map showing in unprecedented detail the large-scale distribution of galaxies between 5 and 8 billion years ago. [abridged]
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