  Differential and double-differential cross sections for the production of top
quark pairs in proton-proton collisions at $\sqrt{s} =$ 13 TeV are measured as
a function of kinematic variables of the top quarks and the top quark-antiquark
($\mathrm{t}\overline{\mathrm{t}}$) system. In addition, kinematic variables
and multiplicities of jets associated with the
$\mathrm{t}\overline{\mathrm{t}}$ 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 $\mathrm{t}\overline{\mathrm{t}}$
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.
