In this thesis, measurements of inclusive and differential Z boson production cross sections in proton-proton collisions at [square root of] s =13 TeV with the CMS detector at Large Hadron Collider are performed with the di-muon channel. The measured total inclusive cross section times branching ratio is or(pp - ZX) x [beta](Z --> [mu][mu]) = 1870 ± 2(stat) ± 35(syst) ± 51(lumi) pb for the di-muon invariant mass in the range of 60 to 120 GeV, which is in good agreement with the next-to-next-to leading order QCD predictions. The spectra of Z boson transverse momentum, ... variable, rapidity, and the muon transverse momentum are also measured and compared with theoretical predictions. The large production cross section of Z boson and good experimental accessibility of final-state muons permit a real-time monitoring of luminosities using the counts of reconstructed Z --> [mu][mu] events. Preliminary results of counting of Z bosons as a luminometer are shown using the entire 2018 data-taking period. A search for beyond Standard Model neutral Higgs bosons decaying to two muons is also presented. No significant excess is observed. A 95% confidence level upper limit is set on ... The exclusion contour is also determined on the parameter phase space in the context of Minimal Supersymmetric Standard Mode representative benchmark scenarios.