This thesis presents the first direct search for lepton flavor violating decays of the recently discovered Higgs boson. The search is performed in the $H \rightarrow \mu \tau_{e}$ and $H \rightarrow \mu \tau_{h}$ decay channels, where $\tau_{e}$ and $\tau_{h}$ denote the electronic and hadronic tau decay channels respectively. The search is performed using the proton-proton collisions data gathered at the Compact Muon Solenoid detector at the Large Hadron Collider. The search uses 19.7 fb$^{-1}$ of $\sqrt{s}$ = 8 TeV data taken in 2012 as well as 2.3 fb$^{-1}$ of $\sqrt{s}$ = 13 TeV data taken in 2015. The limits on the branching fraction $B(H\rightarrow \mu\tau)$ are measured, and the existing limits from indirect searches are reduced by an order of magnitude. This thesis also presents a measurement of the differential cross section of a W boson produced in associated with jets. This measurement was performed with 2.5 fb$^{-1}$ of $\sqrt{s}$ = 13 TeV proton-proton collision data produced by the Large Hadron Collider in 2015 and recorded at the Compact Muon Solenoid detector. Cross sections are computed as a function of jet multiplicity, and the results are compared to theoretical predictions from leading order and next-to-leading order Monte Carlo generators.