  The LIGO-Virgo Collaboration (LVC) detected, on 2017 August 17, an
exceptional gravitational-wave (GW) event temporally consistent within
$\sim\,1.7 \, \rm s$ with the GRB 1708117A observed by Fermi-GBM and INTEGRAL.
The event turns out to be compatible with a neutron star-neutron star (NS-NS)
coalescence that subsequently produced a radio/optical/X-ray transient detected
at later times. We report the main results of the observations by the AGILE
satellite of the GW170817 localization region (LR) and its electromagnetic
(e.m.) counterpart. At the LVC detection time $T_0$, the GW170817 LR was
occulted by the Earth. The AGILE instrument collected useful data before and
after the GW-GRB event because in its spinning observation mode it can scan a
given source many times per hour. The earliest exposure of the GW170817 LR by
the gamma-ray imaging detector (GRID) started about 935 s after $T_0$. No
significant X-ray or gamma-ray emission was detected from the LR that was
repeatedly exposed over timescales of minutes, hours, and days before and after
GW170817, also considering Mini-calorimeter and Super-AGILE data. Our
measurements are among the earliest ones obtained by space satellites on
GW170817 and provide useful constraints on the precursor and delayed emission
properties of the NS-NS coalescence event. We can exclude with high confidence
the existence of an X-ray/gamma-ray emitting magnetar-like object with a large
magnetic field of $10^{15} \, \rm G$. Our data are particularly significant
during the early stage of evolution of the e.m. remnant.
