  The inclusive top quark pair ($t\bar{t}$) production cross-section
$\sigma_{t\bar{t}}$ has been measured in proton$-$proton collisions at
$\sqrt{s}=13$ TeV, using $36.1$ fb$^{-1}$ of data collected in 2015$-$16 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:
\begin{equation}\nonumber \sigma_{t\bar{t}} = 826.4 \pm 3.6\,\mathrm{(stat)}\
\pm 11.5\,\mathrm{(syst)}\ \pm 15.7\,\mathrm{(lumi)}\ \pm
1.9\,\mathrm{(beam)}\,\mathrm{pb}, \end{equation} 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
$m_t^{\mathrm{pole}}$, giving $m_t^{\mathrm{pole}}=173.1^{+2.0}_{-2.1}$ GeV. It
is also combined with measurements at $\sqrt{s}=7$ TeV and $\sqrt{s}=8$ TeV to
derive ratios and double ratios of $t\bar{t}$ 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 compared with predictions from
various Monte Carlo event generators.
