[en] The Large Hadron Collider (LHC) is designed to collide protons at centre-of-mass energies of up to 14 TeV. One of the two general purpose experiments at the LHC is ATLAS, built to probe a broad spectrum of physics processes of the Standard Model of particle physics and beyond. ATLAS is equipped with a muon spectrometer comprising three superconducting air-core toroid magnets and 1150 precision drift tube (MDT) chambers measuring muon trajectories with better than 50 μm position resolution. The accuracy of the space-to-drift-time relationships of the MDT chambers is one of the main contributions to the momentum resolution. In this thesis, an improved method for the calibration of the precision drift tube chambers in magnetic fields has been developed and tested using curved muon track segments. An accuracy of the drift distance measurement of better than 20 μm is achieved leading to negligible deterioration of the muon momentum resolution. The second part of this work is dedicated to the study of the lepton flavour violating decay τ→μμμ. Lepton flavour violation is predicted by almost every extension of the Standard Model. About 10¹²τ leptons are produced per year at an instantaneous luminosity of 10³³ cm^-2s^-1 and a centre-of-mass energy of 14 TeV. Simulated data samples have been used to evaluate the sensitivity of the ATLAS experiment for τ→μμμ decays with an integrated luminosity of 10 fb^-1. Taking theoretical and experimental systematic uncertainties into account an upper limit on the signal branching ratio of B(τ→μμμ) <5.9 x 10^-7 at 90% confidence level is achievable. This result represents the first estimation in ATLAS. (orig.)