<p>The CERN Large Hadron Collider (LHC) offers a unique opportunity to test the Standard Model of particle physics. The Standard Model predicts the existence of a Higgs boson and provides accurate estimates for the strength of the interactions of the Higgs boson with other particles. After the discovery of the Higgs boson, the measurement of its properties, such as its couplings to other particles, is of paramount importance. </p> <p>The projects described in this thesis explore different aspects of one of such measurements – the search for the Higgs boson decay into a pair of muons (H→<em>μμ</em>), conducted by the CMS experiment at the LHC. This decay plays an important role in elementary particle physics, as it provides a direct way to measure the coupling of the Higgs boson to the muon. The first evidence of the H→<em>μμ</em> decay was reported in 2020 as a result of an elaborate statistical analysis of the dataset collected by the CMS experiment during Run 2 of the LHC (2016–2018). The observed (expected) upper limit on the signal strength modifier for this decay at 95% confidence level was found to be 1.93 (0.81), constituting the most precise measurement to date. </p> <p>The details of this analysis, along with studies to establish possible directions for the development of the next iteration of  the H→<em>μμ</em> analysis using Run 3 data, are discussed in this thesis. In addition, a novel machine learning-based algorithm for the muon high level trigger is presented, which ultimately improves the data-taking efficiency of the CMS experiment, and hence, helps to increase the sensitivity of future H→<em>μμ</em> searches. Finally, projections of the H→<em>μμ</em> search sensitivity to the data-taking conditions at the High-Luminosity Large Hadron Collider are presented, estimating the achievable precision for future measurements of the Higgs boson properties.</p>