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This paper describes precision measurements of the transverse momentum$p_\mathrm{T}^{\ell\ell}$ ($\ell=e,\mu$) and of the angular variable$\phi^{*}_{\eta}$ distributions of Drell-Yan lepton pairs in a mass range of66-116 GeV. The analysis uses data from 36.1 fb$^{-1}$ of proton-protoncollisions at a centre-of-mass energy of $\sqrt{s}=13$ TeV collected by theATLAS experiment at the LHC in 2015 and 2016. Measurements in electron-pair andmuon-pair final states are performed in the same fiducial volumes, correctedfor detector effects, and combined. Compared to previous measurements inproton-proton collisions at $\sqrt{s}=$7 and 8 TeV, these new measurementsprobe perturbative QCD at a higher centre-of-mass energy with a differentcomposition of initial states. They reach a precision of 0.2% for thenormalized spectra at low values of $p_\mathrm{T}^{\ell\ell}$. The data arecompared with different QCD predictions, where it is found that predictionsbased on resummation approaches can describe the full spectrum withinuncertainties.

Measurement of the transverse momentum distribution of Drell-Yan lepton  pairs in proton-proton collisions at $\sqrt{s}=13$ TeV with the ATLAS  detector