A measurement of the
W
+
W
−
boson pair production cross section in proton-proton collisions at
√
s
=
13
 
 
TeV
is presented. The data used in this study are collected with the CMS detector at the CERN LHC and correspond to an integrated luminosity of
35.9
 
 
fb
−
1
. The
W
+
W
−
candidate events are selected by requiring two oppositely charged leptons (electrons or muons). Two methods for reducing background contributions are employed. In the first one, a sequence of requirements on kinematic quantities is applied allowing a measurement of the total production cross section,
117.6
±
6.8
 
 
pb
, which agrees well with the theoretical prediction. Fiducial cross sections are also reported for events with zero or one jet, and the change in the zero-jet fiducial cross section with the jet transverse momentum threshold is measured. Normalized differential cross sections are reported within the fiducial region. A second method for suppressing background contributions employs two random forest classifiers. The analysis based on this method includes a measurement of the total production cross section and also a measurement of the normalized jet multiplicity distribution in
W
+
W
−
events. Finally, a dilepton invariant mass distribution is used to probe for physics beyond the standard model in the context of an effective field theory, and constraints on the presence of dimension-6 operators are derived.