The Compact Muon Solenoid (CMS) detector has successfully operated with the Large Hadron Collider (LHC) collisions since 2010, leading to the Higgs boson discovery in 2012 by the CMS and ATLAS collaborations. The analyses of data taken during Run 2 (2016-2018) has already led to many interesting results about the properties of the Higgs boson and for the most part they are compatible in the context of the standard model (SM) so far. These studies are important because the SM appears to be an approximation of a more general theory. Precise studies of the Higgs boson's interactions with the known matter and force particles are essential to reveal the microscopic deviations from the SM prediction. One of such interactions is Yukawa couplings of the Higgs boson and fermions. The H → [tau tau] decay is the most sensitive fermionic decay mode that allows direct probing of this interaction. This thesis presents a study of the Higgs boson properties by observing its decay to a pair of tau leptons and testing evidence of non-SM interactions in the Higgs boson production. The results exploit the data collected by the CMS detector during LHC Run-2, in proton-proton collisions with a center-of-mass energy of 13 TeV. Firstly, the Higgs bosons' properties were explored by two complementary approaches by measuring its cross sections. Thanks to the observation of the H → [tau tau] decay in 2016, we can measure the total cross section with higher precision. Furthermore, in the first analysis, the cross sections of different Higgs productions were scrutinized using fine selections within each Higgs production mode which are mutually exclusive using the Simplified Template Cross Section (STXS) framework, proposed by the LHC Higgs Cross Section Working Group. In the second analysis, the first-ever measurement of the inclusive and differential fiducial cross sections for the Higgs boson production decaying to a pair of tau leptons was presented. In the third analysis, a search for anomalous couplings in the Higgs production vertex, including Charge-Parity (CP) violating couplings, is also performed targeting Higgs boson production via gluon fusion in association with two jets and vector boson fusion. None of these analyses has found any hint of new physics beyond the SM, but stringent limits on anomalous Higgs boson couplings to data were set and cross sections of the Higgs bosons in smaller phase spaces were precisely measured.