The inclusive top quark pair (tt) production cross-section σ tt has been measured in proton-proton collisions at √ s = 13 TeV, 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: σ 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 m pole t , giving m pole t = 173.1 +2.0 −2.1 GeV. It is also combined with measurements at √ s = 7 TeV and √ s = 8 TeV 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 singlelepton and dilepton kinematic variables, and the results are compared with predictions from various Monte Carlo event generators.