A measurement of the W W boson pair production cross section in proton-proton collisions at $\sqrt{s}$ = 13 TeV is presented. The data used in this study were collected with the CMS detector at the LHC and correspond to an integrated luminosity of 35.9 fb$^{-1}$. The W$^+$ W$^-$ candidate events are selected by first 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 cross section: 117.6 +/- 6.8 pb which agrees well with the theoretical cross section. Fiducial cross sections are also reported for events with zero jets or one jet, and the change in the zero-jet fiducial cross sec- tion with the jet $p_T$ threshold is measured. Normalized differential cross sections are reported within the fiducial region; these are compared to theoretical predictions based on quantum chromodynamics at next-to-next-to-leading-order accuracy. A second method for suppressing background contributions employs two random forest classifiers. The analysis based on this method includes a measurement of the total 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 limits on the presence of dimension-6 operators are derived.