AbstractThe VIMOS Public Extragalactic Redshift Survey [VIPERS, Guzzo et al. 2014] is using the VIMOS spectrograph at the ESO VLT to measure redshifts for ∼ 100,000 galaxies with I_AB < 22.5 and 0.5 < z < 1.2, over an area of 24 deg² (split over the W1 and W4 fields of CFHTLS). VIPERS currently provides, at such redshifts, the best compromise between volume, number of galaxies and dense spatial sampling. We present here the first estimate of the power spectrum of the galaxy distribution, P(k), at redshifts z ∼ 0.75 and z ∼ 1, obtained from the ∼ 55,000 redshifts of the PDR-1 data release. We discuss first constraints on cosmological quantities, as the matter density and the baryonic fraction, obtained for the first time at an epoch when the Universe was about half its current age.