  The discovery of the first electromagnetic counterpart to a gravitational
wave signal has generated follow-up observations by over 50 facilities
world-wide, ushering in the new era of multi-messenger astronomy. In this
paper, we present follow-up observations of the gravitational wave event
GW170817 and its electromagnetic counterpart SSS17a/DLT17ck (IAU label
AT2017gfo) by 14 Australian telescopes and partner observatories as part of
Australian-based and Australian-led research programs. We report early- to
late-time multi-wavelength observations, including optical imaging and
spectroscopy, mid-infrared imaging, radio imaging, and searches for fast radio
bursts. Our optical spectra reveal that the transient source afterglow cooled
from approximately 6400K to 2100K over a 7-day period and produced no
significant optical emission lines. The spectral profiles, cooling rate, and
photometric light curves are consistent with the expected outburst and
subsequent processes of a binary neutron star merger. Star formation in the
host galaxy probably ceased at least a Gyr ago, although there is evidence for
a galaxy merger. Binary pulsars with short (100 Myr) decay times are therefore
unlikely progenitors, but pulsars like PSR B1534+12 with its 2.7 Gyr
coalescence time could produce such a merger. The displacement (about 2.2 kpc)
of the binary star system from the centre of the main galaxy is not unusual for
stars in the host galaxy or stars originating in the merging galaxy, and
therefore any constraints on the kick velocity imparted to the progenitor are
poor.
