Abstract Single- and double-differential cross-section measurements are presented for the production of top-quark pairs, in the lepton + jets channel at particle and parton level. Two topologies, resolved and boosted, are considered and the results are presented as a function of several kinematic variables characterising the top and $$t\bar{t}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>t</mml:mi> <mml:mover> <mml:mrow> <mml:mi>t</mml:mi> </mml:mrow> <mml:mrow> <mml:mo>¯</mml:mo> </mml:mrow> </mml:mover> </mml:mrow> </mml:math> system and jet multiplicities. The study was performed using data from pp collisions at centre-of-mass energy of 13 TeV collected in 2015 and 2016 by the ATLAS detector at the CERN Large Hadron Collider (LHC), corresponding to an integrated luminosity of $$36~\mathrm {fb}^{-1}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mn>36</mml:mn> <mml:mspace/> <mml:msup> <mml:mrow> <mml:mi>fb</mml:mi> </mml:mrow> <mml:mrow> <mml:mo>-</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:msup> </mml:mrow> </mml:math> . Due to the large $$t\bar{t}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>t</mml:mi> <mml:mover> <mml:mrow> <mml:mi>t</mml:mi> </mml:mrow> <mml:mrow> <mml:mo>¯</mml:mo> </mml:mrow> </mml:mover> </mml:mrow> </mml:math> cross-section at the LHC, such measurements allow a detailed study of the properties of top-quark production and decay, enabling precision tests of several Monte Carlo generators and fixed-order Standard Model predictions. Overall, there is good agreement between the theoretical predictions and the data.