Tests of Lepton Flavour Universality using semitauonic B decays in the LHCb experiment at CERN

The LHCb experiment foresees a new era of high luminosity, aiming to clarify persistent tensions between experiments and the SM predictions, such as those related to the flavour sector. This thesis is devoted to the measurement of the LFU ratios R(D0) and R(D*0), with the 3-prong hadronic tau decay modes, using LHCb Run 2 data. Even though the final result is blinded and the systematics uncertainties need to be computed, the signal branching fraction are obtained with a competitive precision. Moreover, the computation of the statistical and external uncertainties of the R(D(*)0) ratios hints that the analysis documented here will be a relevant measurement in the LFU sector. Furthermore, a contribution to the LHCb detector upgrade is documented, based on testing the new hybrid pixel VELO sensors' performance.