Abstract Normalised multi-differential cross sections for top quark pair ($$\hbox {t}{\bar{\hbox {t}}}$$ tt¯ ) production are measured in proton-proton collisions at a centre-of-mass energy of 13$$\,{\text {TeV}}$$ TeV using events containing two oppositely charged leptons. The analysed data were recorded with the CMS detector in 2016 and correspond to an integrated luminosity of $$35.9{\,{\text {fb}}^{-1}} $$ 35.9fb-1 . The double-differential $$\hbox {t}{\bar{\hbox {t}}}$$ tt¯ cross section is measured as a function of the kinematic properties of the top quark and of the $$\hbox {t}{\bar{\hbox {t}}}$$ tt¯ system at parton level in the full phase space. A triple-differential measurement is performed as a function of the invariant mass and rapidity of the $$\hbox {t}{\bar{\hbox {t}}}$$ tt¯ system and the multiplicity of additional jets at particle level. The data are compared to predictions of Monte Carlo event generators that complement next-to-leading-order (NLO) quantum chromodynamics (QCD) calculations with parton showers. Together with a fixed-order NLO QCD calculation, the triple-differential measurement is used to extract values of the strong coupling strength $$\alpha _{S}$$ αS and the top quark pole mass ($$m_{{\text {t}}}^{{\text {pole}}}$$ mtpole ) using several sets of parton distribution functions (PDFs). The measurement of $$m_{{\text {t}}}^{{\text {pole}}}$$ mtpole exploits the sensitivity of the $$\hbox {t}{\bar{\hbox {t}}}$$ tt¯ invariant mass distribution to $$m_{{\text {t}}}^{{\text {pole}}}$$ mtpole near the production threshold. Furthermore, a simultaneous fit of the PDFs, $$\alpha _{S}$$ αS , and $$m_{{\text {t}}}^{{\text {pole}}}$$ mtpole is performed at NLO, demonstrating that the new data have significant impact on the gluon PDF, and at the same time allow an accurate determination of $$\alpha _{S}$$ αS and $$m_{{\text {t}}}^{{\text {pole}}}$$ mtpole . The values $$\alpha _{S}(m_{{\text {Z}}}) = 0.1135{}^{+0.0021}_{-0.0017}$$ αS(mZ)=0.1135-0.0017+0.0021 and $$m_{{\text {t}}}^{{\text {pole}}} = 170.5 \pm 0.8 \,{\text {GeV}} $$ mtpole=170.5±0.8GeV are extracted, which account for experimental and theoretical uncertainties, the latter being estimated from NLO scale variations. Possible effects from Coulomb and soft-gluon resummation near the $$\hbox {t}{\bar{\hbox {t}}}$$ tt¯ production threshold are neglected in these parameter extractions. A rough estimate of these effects indicates an expected correction of $$m_{{\text {t}}}^{{\text {pole}}}$$ mtpole of the order of $$+1 \,{\text {GeV}} $$ +1GeV , which can be regarded as additional theoretical uncertainty in the current $$m_{{\text {t}}}^{{\text {pole}}}$$ mtpole extraction.