We present the Survey for High-z Absorption Red and Dead Sources (SHARDS), an ESO/GTC Large Program carried out using the OSIRIS instrument on the 10.4m Gran Telescopio Canarias (GTC). SHARDS is an ultra-deep optical spectro-photometric survey of the GOODS-N field covering 130arcmin2 at wavelengths between 500 and 950nm with 24 contiguous medium-band filters (providing a spectral resolution R~50). The data reach an AB magnitude of 26.5 (at least at a 3{sigma} level) with sub-arcsec seeing in all bands. SHARDS' main goal is to obtain accurate physical properties of intermediate- and high-z galaxies using well-sampled optical spectral energy distributions (SEDs) with sufficient spectral resolution to measure absorption and emission features, whose analysis will provide reliable stellar population and active galactic nucleus (AGN) parameters. Among the different populations of high-z galaxies, SHARDS' principal targets are massive quiescent galaxies at z>1, whose existence is one of the major challenges facing current hierarchical models of galaxy formation. In this paper, we outline the observational strategy and include a detailed discussion of the special reduction and calibration procedures which should be applied to the GTC/OSIRIS data. An assessment of the SHARDS data quality is also performed. We present science demonstration results on the detection and study of emission-line galaxies (star-forming objects and AGNs) at z=0-5. We also analyze the SEDs for a sample of 27 quiescent massive galaxies with spectroscopic redshifts in the range 1.0<z<~1.4.