The surface detector array of the Pierre Auger Observatory can detect neutrinos with energy E ?? between 1017 eV and 1020 eV from point-like sources across the sky south of +55° and north of ???65° declinations. A search has been performed for highly inclined extensive air showers produced by the interaction of neutrinos of all flavors in the atmosphere (downward-going neutrinos), and by the decay of tau leptons originating from tau neutrino interactions in Earth's crust (Earth-skimming neutrinos). No candidate neutrinos have been found in data up to 2010 May 31. This corresponds to an equivalent exposure of ~3.5 years of a full surface detector array for the Earth-skimming channel and ~2 years for the downward-going channel. An improved up...