  Muons produced in atmospheric cosmic ray showers account for the by far
dominant part of the event yield in large-volume underground particle
detectors. The IceCube detector, with an instrumented volume of about a cubic
kilometer, has the potential to conduct unique investigations on atmospheric
muons by exploiting the large collection area and the possibility to track
particles over a long distance. Through detailed reconstruction of energy
deposition along the tracks, the characteristics of muon bundles can be
quantified, and individual particles of exceptionally high energy identified.
The data can then be used to constrain the cosmic ray primary flux and the
contribution to atmospheric lepton fluxes from prompt decays of short-lived
hadrons.
  In this paper, techniques for the extraction of physical measurements from
atmospheric muon events are described and first results are presented. The
multiplicity spectrum of TeV muons in cosmic ray air showers for primaries in
the energy range from the knee to the ankle is derived and found to be
consistent with recent results from surface detectors. The single muon energy
spectrum is determined up to PeV energies and shows a clear indication for the
emergence of a distinct spectral component from prompt decays of short-lived
hadrons. The magnitude of the prompt flux, which should include a substantial
contribution from light vector meson di-muon decays, is consistent with current
theoretical predictions.
