The muon and anti-muon neutrino energy spectrum is determined from 2000-2003 AMANDA telescope data using regularised unfolding. This is the first measurement of atmospheric neutrinos in the energy range 2-200 TeV. The result is compared to different atmospheric neutrino models and it is compatible with the atmospheric neutrinos from pion and kaon decays. No significant contribution from charm had-ron decays or extraterrestrial neutrinos is detected. The capabilities to improve the measurement of the neutrino spectrum with the successor experiment IceCube are discussed. (c) 2010 Elsevier B.V. All rights reserved.