  A search for high-energy neutrinos interacting within the IceCube detector
between 2010 and 2012 provided the first evidence for a high-energy neutrino
flux of extraterrestrial origin. Results from an analysis using the same
methods with a third year (2012-2013) of data from the complete IceCube
detector are consistent with the previously reported astrophysical flux in the
100 TeV - PeV range at the level of $10^{-8}\, \mathrm{GeV}\,
\mathrm{cm}^{-2}\, \mathrm{s}^{-1}\, \mathrm{sr}^{-1}$ per flavor and reject a
purely atmospheric explanation for the combined 3-year data at $5.7 \sigma$.
The data are consistent with expectations for equal fluxes of all three
neutrino flavors and with isotropic arrival directions, suggesting either
numerous or spatially extended sources. The three-year dataset, with a livetime
of 988 days, contains a total of 37 neutrino candidate events with deposited
energies ranging from 30 to 2000 TeV. The 2000 TeV event is the highest-energy
neutrino interaction ever observed.
