  A measurement of inclusive four-jet production in proton-proton collisions at
a center-of-mass energy of 13 TeV is presented. The transverse momenta of jets
within $\lvert\eta\rvert$ $\lt$ 4.7 reach down to 35, 30, 25, and 20 GeV for
the first-, second-, third-, and fourth-leading jet, respectively. Differential
cross sections are measured as functions of the jet transverse momentum, jet
pseudorapidity, and several other observables that describe the angular
correlations between the jets. The measured distributions show sensitivity to
different aspects of the underlying event, parton shower, and matrix element
calculations. In particular, the interplay between angular correlations caused
by parton shower and double-parton scattering contributions is shown to be
important. The double-parton scattering contribution is extracted by means of a
template fit to the data, using distributions for single-parton scattering
obtained from Monte Carlo event generators and a double-parton scattering
distribution constructed from inclusive single-jet events in data. The
effective double-parton scattering cross section is calculated and discussed in
view of previous measurements and of its dependence on the models used to
describe the single-parton scattering background.
