The low mass Drell-Yan di-muon process is investigated with the ATLAS detector at the LHC, in order to provide information that advances our knowledge of the Parton Density Functions in a region of phase space unaccessible at previous experiments. A cut-based selection of di-muon events is performed, using 2010 data with a centre of mass energy of the proton-proton collisions of 7TeV, and an integrated luminosity of 36 pb−1. The analysis probes the region of low muon transverse momentum (pT > 6GeV), and low di-muon mass region 12 < M < 66GeV. The main challenges of the analysis are the understanding of the muon isolation and the trigger efficiency. In order to reject the large QCD background the analysis relies on stringent isolation criteria. The efficiency of the chosen selection is presented in detail. The second main part of the analysis is the measurement of the trigger efficiency for low pT threshold muon triggers. This is an important aspect of the cross section measurement, since the pT spectrum of leptons from the low mass Drell-Yan process are soft and populate the trigger threshold region. In order to measure the differential cross section in mass d dM in the fiducial region of |η| < 2.4 and pT,μ1 > 9GeV and pT,μ2 > 6GeV (asymmetric analysis) or pT,μ1 > 6GeV and pT,μ2 > 6GeV (symmetric analysis), a one dimensional bin-by-bin unfolding is adopted to account for detector reconstruction and resolution effects; all the associated uncertainties are also presented. The fiducial and extrapolated differential cross sections are measured at the Born level. Dressed level corrections are also given. The measured cross sections are shown to agree with theoretical predictions within the margin of error. A precision of 9.7% is achieved in the asymmetric analysis in the lowest invariant mass bin between 12 and 17GeV; the statistical and systematic uncertainties in the same bin are 4.2% and 8.7% respectively. In the remaining mass region the total uncertainty is smaller. The luminosity error during the 2010 data taking period is estimated to be 3.4%. In addition to the Drell-Yan cross section measurement, the thesis describes the study performed in order to extract the Lorentz angle value in the ATLAS Semiconductor Tracker. The Lorentz angle is computed through the study of the SCT cluster width from both cosmic and collision data and comparison with simulation is shown. The track selection on collision data is defined and the fitting range is optimised to give robust results. Throughout this thesis the convention c = 1 is adopted.