CERN-LHC. Measurements are presented of associated production of a W boson and a charm quark (W + c) in proton-proton collisions at a center-of-mass energy of 13 TeV. The data correspond to an integrated luminosity of 35.7 fb−1 collected by the CMS experiment at the CERN LHC. The W bosons are identified by their decay into a muon and a neutrino. The charm quarks are tagged via the full reconstruction of D∗(2010) mesons that decay via D∗(2010) --> D0 + pi \to K + pi + pi. A cross section is measured in the fiducial region defined by the muon transverse momentum pT(\mu) > 26 GeV, muon pseudorapidity |\eta(\mu)| < 2.4, and charm quark transverse momentum pT(c) > 5 GeV. The cross section is also measured differentially as a function of the pseudorapidity of the muon from the W boson decay, presented separately for W+, W- and the combination. The W + D∗(2010) cross section is determined with the additional constraint of |\eta(D*)| < 2.4 and without imposing restrictions on the origin of the D∗(2010) meson.