  The leptonic and inclusive hadronic decay branching fractions of the W boson
are measured using proton-proton collision data collected at $\sqrt{s} =$ 13
TeV by the CMS experiment at the CERN LHC, corresponding to an integrated
luminosity of 35.9 fb$^{-1}$. Events characterized by the production of one or
two W bosons are selected and categorized based on the multiplicity and flavor
of reconstructed leptons, the number of jets, and the number of jets identified
as originating from the hadronization of b quarks. A binned maximum likelihood
estimate of the W boson branching fractions is performed simultaneously in each
event category. The measured branching fractions of the W boson decaying into
electron, muon, and tau lepton final states are (10.83 $\pm$ 0.10)%, (10.94
$\pm$ 0.08)%, and (10.77 $\pm$ 0.21)%, respectively, consistent with lepton
flavor universality for the weak interaction. The average leptonic and
inclusive hadronic decay branching fractions are estimated to be (10.89 $\pm$
0.08)% and (67.32 $\pm$ 0.23)%, respectively. Based on the hadronic branching
fraction, three standard model quantities are subsequently derived: the sum of
squared elements in the first two rows of the Cabibbo-Kobayashi-Maskawa (CKM)
matrix $\sum_{ij}\vert V_{ij}\vert^{2}$ = 1.984 $\pm$ 0.021, the CKM element
$\vert V_\mathrm{cs}\vert$ = 0.967 $\pm$ 0.011, and the strong coupling
constant at the W boson mass scale, $\alpha_\mathrm{S}(m^2_\mathrm{W})$ = 0.095
$\pm$ 0.033.
