Three measurements of top-quark pair production cross sections in proton-proton collisions at sqrt(s) = 13 TeV using data collected by the ATLAS experiment are presented. The single-lepton final states are used, where one electron or muon, two b-jets and two other jets can be identified. The inclusive ttbar production cross section is measured to be sigma(ttbar) = 817 +/- 13 (stat.) +/- 103 (syst.) +/- 88 (lum.) pb, which is in good agreement with predictions and with other measurements. Absolute and relative differential cross sections of ttbar production are also measured, showing an overall good agreement with predictions, except for the top-quark transverse momentum distribution. As already reported in measurements at lower proton-proton collision energies, this distribution is shifted towards higher momenta in all predictions with respect to the observations. Total and differential fiducial cross sections of ttbar production in association with heavy-flavour jets are also presented. All tested models are found to agree with data within the uncertainties of these measurements.