  Production cross sections of the Higgs boson are measured in the
H$\to$ZZ$\to4\ell$ ($\ell=$e,$\mu$) decay channel. A data sample of
proton-proton collisions at a center-of-mass energy of 13 TeV, collected by the
CMS detector at the LHC and corresponding to an integrated luminosity of 137
fb$^{-1}$ is used. The signal strength modifier $\mu$, defined as the ratio of
the Higgs boson production rate in the $4\ell$ channel to the standard model
(SM) expectation, is measured to be $\mu=$ 0.94 $\pm$ 0.07 (stat)
${}^{+0.09}_{-0.08}$ (syst) at a fixed value of $m_\mathrm{H} = $ 125.38 GeV.
The signal strength modifiers for the individual Higgs boson production modes
are also reported. The inclusive fiducial cross section for the H$\to4\ell$
process is measured to be 2.84$^{+0.23}_{-0.22}$ (stat) ${}^{+0.26}_{-0.21}$
(syst) fb, which is compatible with the SM prediction of 2.84 $\pm$ 0.15 fb for
the same fiducial region. Differential cross sections as a function of the
transverse momentum and rapidity of the Higgs boson, the number of associated
jets, and the transverse momentum of the leading associated jet are measured. A
new set of cross section measurements in mutually exclusive categories targeted
to identify production mechanisms and kinematical features of the events is
presented. The results are in agreement with the SM predictions.
