  The surface detector array (SD) of the Pierre Auger Observatory is sensitive
to neutrinos at energies in the 100 PeV to 100 EeV range. This sensitivity,
together with its large acceptance, makes it a complementary detector to other
neutrino telescopes, which have their peak sensitivities at lower energies. The
neutrino-induced air showers that the SD of the Pierre Auger Observatory is
sensitive to can be divided into those induced by interactions of neutrinos of
any flavor deep in the atmosphere, and those induced by charged-current
interactions of tau neutrinos in the Earth's crust. Both of these types can be
efficiently distinguished from cosmic ray-induced air showers, provided that
their zenith angles are larger than 60{\deg}. As no neutrino candidates were
found in the performed searches, we present limits on the diffuse all-flavor
neutrino flux. Using these limits, we obtained constraints on cosmic-ray and
neutrino production models. In the light of the recent observations of
gravitational waves (GW), we also present the follow-up of LIGO/Virgo GW
events. These include binary black hole merger events and also GW170817, the
only binary neutron star merger ever observed directly.
