Abstract: Extragalactic surveys are a key tool for better understanding the evolution of galaxies. Both deep and wide-field surveys serve to provide a clearer emerging picture of the physical processes that take place in and around galaxies, and to identify which of these processes are the most important in shaping the properties of galaxies. Aims. The Lockman Spectroscopic Redshift Survey using Osiris (Lockman-SpReSO) aims to provide one of the most complete optical spectroscopic follow-ups of the far-infrared (FIR) sources detected by the Herschel Space Observatory in the Lockman Hole (LH) field. The optical spectroscopic study of the FIR-selected galaxies supplies valuable information about the relation between fundamental FIR and optical parameters, including extinction, star formation rate, and gas metallicity. In this article, we introduce and provide an in-depth description of the Lockman-SpReSO project and of its early results. Methods. We selected FIR sources from Herschel observations of the central 24 arcmin A - 24 arcmin of the LH field with an optical counterpart up to 24.5 RC(AB). The sample comprises 956 Herschel FIR sources, plus 188 additional interesting objects in the field. These are point X-ray sources, cataclysmic variable star candidates, high-velocity halo star candidates, radio sources, very red quasi-stellar objects, and optical counterparts of sub-millimetre galaxies. The faint component of the catalogue (RC(AB) ? 20) was observed using the OSIRIS instrument on the 10.4 m Gran Telescopio Canarias in multi-object spectroscopy (MOS) mode. The bright component was observed using two multi-fibre spectrographs: the AF2-WYFFOS at the William Herschel Telescope and the HYDRA instrument at the WYIN telescope. Results. From an input catalogue of 1144 sources, we measured a secure spectroscopic redshift in the range 0.03 ? z ? 4.96 for 357 sources with at least two identified spectral lines. In addition, for 99 sources that show only one emission or absorption line, a spectroscopic redshift was postulated based on the line and object properties, and photometric redshift. In both cases, properties of emission and absorption lines were measured. Furthermore, to characterize the sample in more depth with determined spectroscopic redshifts, spectral energy distribution (SED) fits were performed using the CIGALE software. The IR luminosity and the stellar mass estimations for the sample are also presented as a preliminary description.

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