  Measurements of Higgs boson production, where the Higgs boson decays into a
pair of $\tau$ leptons, are presented, using a sample of proton-proton
collisions collected with the CMS experiment at a center-of-mass energy of 13
TeV, corresponding to an integrated luminosity of 138 fb$^{-1}$. Three analyses
are presented. Two are targeting Higgs boson production via gluon fusion and
vector boson fusion: a neural network based analysis and an analysis based on
an event categorization optimized on the ratio of signal over background
events. These are complemented by an analysis targeting vector boson associated
Higgs boson production. Results are presented in the form of signal strengths
relative to the standard model predictions and products of cross sections and
branching fraction to $\tau$ leptons, in up to 16 different kinematic regions.
For the simultaneous measurements of the neural network based analysis and the
analysis targeting vector boson associated Higgs boson production signal
strengths are found to be 0.82 $\pm$ 0.11 for inclusive Higgs boson production,
0.67 $\pm$ 0.19 (0.81 $\pm$ 0.17) for the production mainly via gluon fusion
(vector boson fusion), and 1.79 $\pm$ 0.45 for vector boson associated Higgs
boson production.
