The study of correlations between observations of different messengers from extreme sources of the Universe has emerged as an outstanding way to make progress in astrophysics. The Pierre Auger Observatory is capable of significant contributions as an ultra-high energy particle detector, particularly through its capability to search for inclined showers produced by neutrinos. We describe the neutrino searches made with the Observatory with particular emphasis on the recent results following the detections of gravitational waves from binary mergers with Advanced LIGO and VIRGO, leading to competitive limits.