(Abridged) We present the Survey for High-z Absorption Red and Dead Sources (SHARDS), an ESO/GTC Large Program carried out with GTC/OSIRIS. SHARDS is an ultra-deep optical spectro-photometric survey of the GOODS-N field (130 arcmin^2) at wavelengths 500 to 950 nm and using 24 contiguous medium-band filters (spectral resolution R 50). The data reach 26.5 mag (>3-sigma level) with sub-arcsec seeing in all bands. SHARDS main goal is obtaining accurate physical properties of interm- and high-z galaxies using well-sampled optical SEDs with sufficient spectral resolution to measure absorption and emission features. Among the different populations of high-z galaxies, SHARDS principal targets are massive quiescent galaxies at z>1. In this paper, we outline the observational strategy and include a detailed discussion of the special reduction and calibration procedures applied to the GTC/OSIRIS data. We present science demonstration results about the detection and study of emission-line galaxies (star-forming and AGN) at z=0-5. We also analyze the SEDs for a sample of 27 quiescent massive galaxies at 1.0<z<1.4. We discuss on the improvements introduced by the SHARDS dataset in the analysis of their SFH and stellar properties. We discuss the systematics arising from the use of different stellar population libraries. We find that the UV-to-MIR SEDs of the massive quiescent galaxies at z=1.0-1.5 are well described by an exponential decaying SFH with scale tau=100-200 Myr, age 1.5-2.0 Gyr, solar or slightly sub-solar metallicity, and moderate extinction, A(V)~0.5 mag. We also find that galaxies with masses above M* are typically older than lighter galaxies, as expected in a downsizing scenario of galaxy formation. This trend is, however, model dependent, i.e., it is significantly more evident in the results obtained with some stellar population synthesis libraries and almost absent in others.
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