The inclusive top quark pair (tt¯) production cross-section σtt¯ 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 eμ pair and b-tagged jets, the cross-section is measured to be: σtt¯=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.