The LHCb experiment at the Large Hadron Collider is designed for studying the properties of heavy quarks and CP violation to indirectly search for new physics beyond the Standard Model. The first topic of this dissertation is a study of semitauonic B_c meson decays at LHCb to test the universality of the couplings of charged leptons in electroweak interactions, which is known as lepton flavor universality in the Standard Model. The second topic of this dissertation is the development of readout electronics for a new silicon-strip tracking detector, the Upstream Tracker, to upgrade the LHCb detector. The upgraded LHCb detector will collect much more data in the upcoming runs of the Large Hadron Collider.