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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 photomultiplier tubes buried deep in the polar ice between 1500 m and 2000 m. 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 photomultipliers. 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 • accuracy.