  The first observational run of the Advanced LIGO detectors, from September
12, 2015 to January 19, 2016, saw the first detections of gravitational waves
from binary black hole mergers. In this paper we present full results from a
search for binary black hole merger signals with total masses up to $100
M_\odot$ and detailed implications from our observations of these systems. Our
search, based on general-relativistic models of gravitational wave signals from
binary black hole systems, unambiguously identified two signals, GW150914 and
GW151226, with a significance of greater than $5\sigma$ over the observing
period. It also identified a third possible signal, LVT151012, with
substantially lower significance, and with an 87% probability of being of
astrophysical origin. We provide detailed estimates of the parameters of the
observed systems. Both GW150914 and GW151226 provide an unprecedented
opportunity to study the two-body motion of a compact-object binary in the
large velocity, highly nonlinear regime. We do not observe any deviations from
general relativity, and place improved empirical bounds on several high-order
post-Newtonian coefficients. From our observations we infer stellar-mass binary
black hole merger rates lying in the range $9-240 \mathrm{Gpc}^{-3}
\mathrm{yr}^{-1}$. These observations are beginning to inform astrophysical
predictions of binary black hole formation rates, and indicate that future
observing runs of the Advanced detector network will yield many more
gravitational wave detections.
