With the Surface Detector array (SD) of the Pierre Auger Observatory we can detect neutrinos with energy between 1017 eV and 1020 eV from point-like sources across the sky, from close to the Southern Celestial Pole up to 60o in declination, with peak sensitivities at declinations around ∼ −53o and ∼+55o, and an unmatched sensitivity for arrival directions in the Northern hemisphere. A search has been performed for highly-inclined air showers induced by neutrinos of all flavours with no candidate events found in data taken between 1 Jan 2004 and 31 Aug 2018. Upper limits on the neutrino flux from point-like steady sources have been derived as a function of source declination. An unrivaled sensitivity is achieved in searches for transient sources with emission lasting over an hour or less, if they occur within the field of view corresponding to the zenith angle range between 60o and 95o where the SD of the Pierre Auger Observatory is most sensitive to neutrinos.