  The Antarctic Muon And Neutrino Detector Array (AMANDA) is a high-energy
neutrino telescope operating at the geographic South Pole. It is a lattice of
photo-multiplier tubes buried deep in the polar ice between 1500m and 2000m.
The primary goal of this detector is to discover astrophysical sources of high
energy neutrinos. A high-energy muon neutrino coming through the earth from the
Northern Hemisphere can be identified by the secondary muon moving upward
through the detector. The muon tracks are reconstructed with a maximum
likelihood method. It models the arrival times and amplitudes of Cherenkov
photons registered by the photo-multipliers. This paper describes the different
methods of reconstruction, which have been successfully implemented within
AMANDA. Strategies for optimizing the reconstruction performance and rejecting
background are presented. For a typical analysis procedure the direction of
tracks are reconstructed with about 2 degree accuracy.
