  The IceCube Collaboration has previously discovered a high-energy
astrophysical neutrino flux using neutrino events with interaction vertices
contained within the instrumented volume of the IceCube detector. We present a
complementary measurement using charged current muon neutrino events where the
interaction vertex can be outside this volume. As a consequence of the large
muon range the effective area is significantly larger but the field of view is
restricted to the Northern Hemisphere. IceCube data from 2009 through 2015 have
been analyzed using a likelihood approach based on the reconstructed muon
energy and zenith angle. At the highest neutrino energies between 191 TeV and
8.3 PeV a significant astrophysical contribution is observed, excluding a
purely atmospheric origin of these events at $5.6\,\sigma$ significance. The
data are well described by an isotropic, unbroken power law flux with a
normalization at 100 TeV neutrino energy of
$\left(0.90^{+0.30}_{-0.27}\right)\times10^{-18}\,\mathrm{GeV^{-1}\,cm^{-2}\,s^{-1}\,sr^{-1}}$
and a hard spectral index of $\gamma=2.13\pm0.13$. The observed spectrum is
harder in comparison to previous IceCube analyses with lower energy thresholds
which may indicate a break in the astrophysical neutrino spectrum of unknown
origin. The highest energy event observed has a reconstructed muon energy of
$(4.5\pm1.2)\,\mathrm{PeV}$ which implies a probability of less than 0.005% for
this event to be of atmospheric origin. Analyzing the arrival directions of all
events with reconstructed muon energies above 200 TeV no correlation with known
$\gamma$-ray sources was found. Using the high statistics of atmospheric
neutrinos we report the currently best constraints on a prompt atmospheric muon
neutrino flux originating from charmed meson decays which is below $1.06$ in
units of the flux normalization of the model in Enberg et al. (2008).
