  Data from the AMANDA-B10 detector taken during the austral winter of 1997
have been searched for a diffuse flux of high energy extraterrestrial
muon-neutrinos, as predicted from, e.g., the sum of all active galaxies in the
universe. This search yielded no excess events above those expected from the
background atmospheric neutrinos, leading to upper limits on the
extraterrestrial neutrino flux. For an assumed E^-2 spectrum, a 90% classical
confidence level upper limit has been placed at a level E^2 Phi(E) = 8.4 x
10^-7 GeV cm^-2 s^-1 sr^-1 (for a predominant neutrino energy range 6-1000 TeV)
which is the most restrictive bound placed by any neutrino detector. When
specific predicted spectral forms are considered, it is found that some are
excluded.
