The inclusive top quark pair (tt) production cross-section sigma tt has been measured in proton-proton collisions at s=13TeV, using 36.1 fb-1 of data collected in 2015-2016 by the ATLAS experiment at the LHC. Using events with an opposite-charge e mu pair and b-tagged jets, the cross-section is measured to be: sigma tt=826.4 +/- 3.6(stat)+/- 11.5(syst)+/- 15.7(lumi)+/- 1.9(beam)pb,where the uncertainties reflect the limited size of the data sample, experimental and theoretical systematic effects, the integrated luminosity, and the LHC beam energy, giving a total uncertainty of 2.4%. The result is consistent with theoretical QCD calculations at next-to-next-to-leading order. It is used to determine the top quark pole mass via the dependence of the predicted cross-section on mtpole, giving mtpole=173.1-2.1+2.0GeV. It is also combined with measurements at s=7TeV and s=8TeV to derive ratios and double ratios of tt and Z cross-sections at different energies. The same event sample is used to measure absolute and normalised differential cross-sections as functions of single-lepton and dilepton kinematic variables, and the results are compared with predictions from various Monte Carlo event generators.