The elementary particles, their properties and their interactions are described by the SM, which is the theoretical framework constructed for the study of the strong interactions of quarks and gluons and the unified electroweak force and that is based on local gauge invariance. The SM is very successful in giving account of most of the observed phenomena at the microscopic frontier of physics, having been verified and tested in many experiments in the last decades. The SM has also induced the search of novel phenomena, such as the recent discovery of the Higgs boson by the ATLAS and CMS experiments at the LHC. Despite these spectacular successes, there are evidences that the theory cannot be complete since, besides some possible theoretical diseases (the hierarchy problem), it is unable to explain some observed phenomena in nature. First of all, it does not include gravity and its constituents can only account for around 5% of the energy-matter content of our universe and no SM particle can be a candidate to describe dark matter. Furthermore, the observation of neutrino oscillations implies neutrino mass and mixing, incompatible with the minimal version of the SM. And, in addition, the standard flavour physics framework for CP violation, the mismatch between weak interaction and mass eigenstates of quarks by means of the CKM mixing matrix, is unable to explain the baryon asymmetry of the universe by many orders of magnitude. Although precision experiments in the K and B meson facilities agree with the predictions of the SM, new physics sources of CP violation are unavoidable. With all this, it is clear that extensions of the SM are needed. New physics models that modify the SM in ways subtle enough to be consistent with existing data are being proposed. In this thesis, an extension of the SM with additional sources of CP violation in the top quark sector is proposed. The top quark decays almost exclusively into a b quark and a W boson via the weak interaction, thus it allows to probe the chiral structure of the W-t-b interaction. The Wtb vertex can be parametrised with using an effective Lagrangian approach including the couplings VL, VR, gL ad gR (left- and right-handed vector and tensor couplings) which are in general complex. At tree level in the SM, the coupling VL is given by the CKM matrix element Vtb and is therefore almost equal to one, while the other three couplings (so-called anomalous couplings) vanish, leading to the pure vector minus axial structure of the weak interaction in the SM. Although non-vanishing values of the right-handed coupling VR and of the tensor couplings gR and gL are not forbidden, several constraints on these anomalous couplings exist from both indirect observations and direct measurements. Deviations from the expected values can be probed by measuring the W polarisation fractions or angular asymmetries in the decay products of top quarks. Indeed, the W helicity fractions measured in top quark pairs events have allowed to set limits to the real part of the anomalous couplings VR, gL and gR. However, they are not sensitive to their complex phases which would imply that the top quark decay has a CP-violating component. For unpolarised top quark production the only meaningful reference direction in the top quark rest frame is the momentum q of the W boson (or -q of the b quark). However for polarised top quarks, such as those produced via electroweak interactions, one can also exploit the spin direction given by st. From these two directions, further references can be defined normal N and transverse T to the plane formed by the W boson momentum direction q and the top quark spin direction st. In a similar way that the helicity angle theta* is defined between the lepton in the W boson rest frame and the W boson momentum, the angles N and T are defined between the lepton and these new directions. In addition, two further sets of W boson polarisation fractions can be defined. The most interesting remark is that the normal set of polarisation fractions (FN+, FN0 and FN-) depend on the imaginary part of the anomalous coupling gR; so observables depending on these will deserve special attention. If CP is conserved in the Wtb vertex, i.e. if all anomalous couplings are real, then FN+ = FN-. A net normal W polarisation (FN+, FN-) can only be produced if CP is violated in the t->Wb decay. This property is unique of the normal direction and is here explored in the decay of polarised top quarks produced through electroweak interaction in proton-proton collisions at the LHC. The measurement of this forward-backward asymmetry AFBN (using t-channel single top quark events) is the major contribution of this thesis. The full 7 TeV dataset collected by the ATLAS detector in 2011 has been analyzed, which corresponds to an integrated luminosity of 4.66 fb-1. Events with an isolated electron or muon, missing transverse momentum and two jets being one tagged as a b-jet have been selected in this analysis. A full reconstruction of the top quark from its decay products is required to define the angle N. In order to understand the modelling of the t-channel single top quark events provided by Monte Carlo generators, studies of the kinematic properties of the final state particles have been conducted and di erent event generators have been compared. A special emphasis has been devoted to determine the W+jets background, that constitutes the dominant background contribution. An in-situ technique has been employed using data events in control regions in order to estimate the number of events of this background in the analysed dataset. Other processes such as multijet events are also estimated with dedicated data-driven methods. Finally, top quark background processes and diboson and Z+jets production are determined from Monte Carlo simulations. A cut-based strategy is followed exploiting the properties of the signal events. The final signal-to-background ratio is close to one. The reconstructed distribution of cos N is affected by the acceptance cuts and detector effects. In order to allow a direct comparison of the experimental measurement with the theoretical prediction, the measured angular distribution must be unfolded, i.e. deconvoluted back to parton level (partons from the hard process). An unfolding technique by inversion of the response matrix has been applied to correct for acceptance and reconstruction e ects which are modelled using t-channel simulated events. In addition, systematic uncertainties in modelling the physics processes and detector e ects have been estimated, being the modelling of top quark processes the largest one. The final asymmetry with its statistical and systematic uncertainties is: AFBN = 0.031 +- 0.065 (stat-) +0.029-0.031 (syst.). The result is dominated by the statistical uncertainty, so improvements are expected using the full 2012 dataset at 8 TeV with four times more statistics. Using the relation between AN FB and Im(gR), it is possible to constrain the allowed regions in the top quark polarisation versus Im(gR) plane. Assuming a value of P = 0:9 for the top quark polarisation, which is the SM prediction for the single top t-channel production, the first experimental limits on Im(gR) are found to be [-0.20; 0.30] at 95% confidence level. Both the asymmetry and the limit are consistent with SM predictions. This measurement involves understanding the process at generator level, a precise determination of the background processes, applying an unfolding procedure and estimating the corresponding systematic uncertainties. At the time of writing this thesis, other analyses to probe the Wtb vertex anomalous couplings in single top quark events with the full 8 TeV dataset are being completed in ATLAS, including studies of other unfolding techniques, in addition to the one explored in this document. The combination of several observables will allow to obtain higher precision and set tighter constraints in the Wtb vertex.In order to achieve the level of accuracy and precision required in these measurements, and to be sensitive to new physics, an excellent understanding of the detector is required. Thus performance studies are crucial to properly calibrate and align the detectors, improve the reconstruction algorithms and minimize systematic uncertainties. Indeed this thesis work includes two performance studies carried out with the first ATLAS data: global cosmic-ray runs recorded during the commissioning period and first proton-proton collisions runs at 7 TeV. In the commissioning period, prior to the first collisions in 2010, millions of cosmic-ray events were recorded and reconstructed in the ATLAS detector, and allowed to test the full operation chain, including data acquisition, reconstruction and analysis software. Most of the studies were focused on understanding the performance of individual subdetectors, while in the work presented in the first part of this thesis the performance of the reconstruction of cosmic-ray muons was studied combining information of all the subdetectors (inner detector, calorimeters and muon spectrometer). The performance of the combined tracking was evaluated by comparing the two reconstructed tracks left by a single cosmic-ray muon passing through the upper and then the lower half of the detector. In addition, the track parameter resolutions were derived using information only from data. Once the LHC delivered the first collisions, the reconstruction of other final state objects could also be studied in detailed. The contribution presented here is focused on the reconstruction of jets, in particular the jet structure. The jet shapes were measured in both regions inside and outside the jet cone, and the fraction of the jet momentum left out of the cone was extracted from them. Both measurements were compared to Monte Carlo predictions. In 2015, the LHC will provide proton-proton collisions at 13-14 TeV and the detectors will resume data-taking, accessing a range of energies never studied before, and giving the opportunity for new exciting discoveries in top quark decays. These data will allow to improve the calibration and reconstruction methods, to carry out more performance studies and to improve the understanding of Monte Carlo generators, to minimize any possible systematic uncertainty and to reach the needed accuracy.