  This paper describes the search for astronomical sources of high-energy
neutrinos using the AMANDA-B10 detector, an array of 302 photomultiplier tubes,
used for the detection of Cherenkov light from upward traveling
neutrino-induced muons, buried deep in ice at the South Pole. The absolute
pointing accuracy and angular resolution were studied by using coincident
events between the AMANDA detector and two independent telescopes on the
surface, the GASP air Cherenkov telescope and the SPASE extensive air shower
array. Using data collected from April to October of 1997 (130.1 days of
livetime), a general survey of the northern hemisphere revealed no
statistically significant excess of events from any direction. The sensitivity
for a flux of muon neutrinos is based on the effective detection area for
through-going muons. Averaged over the Northern sky, the effective detection
area exceeds 10,000 m^2 for E_{mu} ~ 10 TeV. Neutrinos generated in the
atmosphere by cosmic ray interactions were used to verify the predicted
performance of the detector. For a source with a differential energy spectrum
proportional to E_{nu}^{-2} and declination larger than +40 degrees, we obtain
E^2(dN_{nu}/dE) <= 10^{-6}GeVcm^{-2}s^{-1} for an energy threshold of 10 GeV.
