Differential and double-differential cross sections for the production of top quark pairs in proton-proton collisions at s=13 TeV are measured as a function of kinematic variables of the top quarks and the top quark-antiquark (tt) system. In addition, kinematic variables and multiplicities of jets associated with the tt production are measured. This analysis is based on data collected by the CMS experiment at the LHC in 2016 corresponding to an integrated luminosity of 35.8 fb-1. The measurements are performed in the lepton+jets decay channels with a single muon or electron and jets in the final state. The differential cross sections are presented at the particle level, within a phase space close to the experimental acceptance, and at the parton level in the full phase space. The results are compared to several standard model predictions that use different methods and approximations. The kinematic variables of the top quarks and the tt system are reasonably described in general, though none predict all the measured distributions. In particular, the transverse momentum distribution of the top quarks is more steeply falling than predicted. The kinematic distributions and multiplicities of jets are adequately modeled by certain combinations of next-to-leading-order calculations and parton shower models.