  We present the results from three gravitational-wave searches for coalescing
compact binaries with component masses above 1$\mathrm{M}_\odot$ during the
first and second observing runs of the Advanced gravitational-wave detector
network. During the first observing run (O1), from September $12^\mathrm{th}$,
2015 to January $19^\mathrm{th}$, 2016, gravitational waves from three binary
black hole mergers were detected. The second observing run (O2), which ran from
November $30^\mathrm{th}$, 2016 to August $25^\mathrm{th}$, 2017, saw the first
detection of gravitational waves from a binary neutron star inspiral, in
addition to the observation of gravitational waves from a total of seven binary
black hole mergers, four of which we report here for the first time: GW170729,
GW170809, GW170818 and GW170823. For all significant gravitational-wave events,
we provide estimates of the source properties. The detected binary black holes
have total masses between $18.6_{-0.7}^{+3.2}\mathrm{M}_\odot$, and
$84.4_{-11.1}^{+15.8} \mathrm{M}_\odot$, and range in distance between
$320_{-110}^{+120}$ Mpc and $2840_{-1360}^{+1400}$ Mpc. No neutron star - black
hole mergers were detected. In addition to highly significant
gravitational-wave events, we also provide a list of marginal event candidates
with an estimated false alarm rate less than 1 per 30 days. From these results
over the first two observing runs, which include approximately one
gravitational-wave detection per 15 days of data searched, we infer merger
rates at the 90% confidence intervals of $110\, -\, 3840$
$\mathrm{Gpc}^{-3}\,\mathrm{y}^{-1}$ for binary neutron stars and $9.7\, -\,
101$ $\mathrm{Gpc}^{-3}\,\mathrm{y}^{-1}$ for binary black holes assuming fixed
population distributions, and determine a neutron star - black hole merger rate
90% upper limit of $610$ $\mathrm{Gpc}^{-3}\,\mathrm{y}^{-1}$.
