Calibration of the ATLAS Electromagnetic Calorimeter and Measurement of $W$ Boson Properties at $\sqrt{s}$ = 5 and 13 TeV with the ATLAS Detector at the LHC

This thesis consists of two main parts. The first part corresponds to an in-situ calibration of the electromagnetic calorimeter using electrons and positrons from $Z$ boson decays selected from all nominal data samples taken by ATLAS during Run 2 between 2015 and 2018, as well as during special runs, characterised by a low number of interactions per bunch crossing in order to improve the experimental resolution of the recoil measurement of $Z$ and $W$ bosons and of the reconstruction of various kinematic variables needed for the $W$ boson mass determination. The nominal data samples were taken at a center of mass energy of 13 TeV corresponding to an integrated luminosity of about 140 fb$^{-1}$, whereas the special runs were taken at 5 and 13 TeV, corresponding to 258 pb$^{-1}$ and 340 pb$^{-1}$, respectively. The second part is on the measurement of $W$ boson properties using data from the special runs, including a measurement of the transverse momentum of the $W$ boson, a measurement of fiducial, single and double differential cross sections, and a preliminary evaluation of the statistical and experimental uncertainties of the $W$ mass determination.