The study of the top quark is fundamental to the field of particle physics, because its high mass of approximately 173 GeV, the highest in the Standard Model, is close to the electro-weak vacuum expectation value of 246 GeV, which hints to the fact that this particle might be special and it could be the key to unveil physics beyond the Standard Model. Therefore a precise study of the properties and mass of the top quark is necessary. In particular the mass of the top quark, which is a free parameter in the Standard Model, needs to be measured precisely, because it is one of the parameters used to constrain the global fit to check for the validity of the Standard Model and its consistency with the measured data. Also, the measured inclusive t-tbar production cross section can be compared to theoretically predicted values, allowing for a further check of the Standard Model. The t-tbar production total fiducial and inclusive cross section and the t-tbar production absolute and normalised differential cross section for seven different leptonic kinematic variables are measured using the data collected in the ATLAS experiment at a center of mass energy of 13 TeV during the full Run 2 period (2015-2018) with a total integrated luminosity of 139 fb-1. The measurement is performed using dilepton e-mu events with opposite sign and with either one or two associated b-jets. The total t-tbar production fiducial cross section is measured with a total relative uncertainty of 2.34% and the total inclusive t-tbar production cross section with a total relative uncertainty of 2.91%. The value of the total inclusive cross section and the contributions to its uncertainty are as such: sigma_t-tbar = 839.8 +/- 1.3 +/- 16.0 +/- 18.4 pb where the first uncertainty is the statistical one, the second is the luminosity uncertainty and the last is the total systematic uncertainty from all of the other sources other than the luminosity. The normalised differential distributions are used to extract the top pole mass for five leptonic kinematic variables, pT(l+l-), pT(l^+) + pT(l-), pT(l), E(l+) + E(l-), m(l+l-), due to their sensitivity to the mass of the top quark. The extraction is done by comparing the measured distributions to Monte Carlo templates at different top mass values. The results show that the uncertainty on the top pole mass can be reduced compared to previous measurements, thanks to the lower uncertainty on the normalised differential cross section distributions, but the templates used in this thesis are not adequate and more proper templates, including correction to the top pT spectrum and NNLO processes, would improve the results.