We present a comprehensive review of AGILE follow-up observations of the Gravitational Wave (GW) events and the unconfirmed marginal triggers reported in the first LIGO-Virgo (LV) Gravitational Wave Transient Catalog (GWTC-1). For seven GW events and 13 LV triggers, the associated 90% credible region was partially or fully accessible to the AGILE satellite at the T (0); for the remaining events, the localization region was not accessible to AGILE due to passages into the South Atlantic Anomaly, or complete Earth occultations (as in the case of GW170817). A systematic search for associated transients, performed on different timescales and on different time intervals about each event, led to the detection of no gamma-ray counterparts. We report AGILE MCAL upper limit fluences in the 400 keV-100 MeV energy range, evaluated in a time window of T (0) +/- 50 s around each event, as well as AGILE GRID upper limit (UL) fluxes in the 30 MeV-50 GeV energy range, evaluated in a time frame of T (0) +/- 950 s around each event. All ULs are estimated at different integration times and are evaluated within the portions of GW credible region accessible to AGILE at the different times under consideration. We also discuss the possibility of AGILE MCAL to trigger and detect a weak soft-spectrum burst such as GRB 170817A.
