This thesis details the precision measurements of Higgs boson properties at the Compact Muon Solenoid experiment. The measurements use proton-proton collision data at a centre-of-mass energy of 13~TeV, collected during Run 2 of the LHC, corresponding to a total integrated luminosity of 137~\fbinv. Production cross sections and Higgs boson couplings are measured in the diphoton decay channel. Events with two isolated photons are selected and subsequently categorised to target different kinematic regions of the Higgs boson production phase-space. The total Higgs boson signal-strength, relative to the Standard Model prediction, is measured to be $1.12 \pm 0.09$. Other properties of the Higgs boson are measured. This includes a simultaneous measurement of 27 independent kinematic regions, representing the most granular measurement of Higgs boson production in a single decay channel to-date.
Following this, a beyond-the-Standard Model interpretation of Higgs boson cross section measurements is provided. The interpretation is performed in an effective field theory framework, which benefits from being agnostic to the specifics of the complete beyond-the-Standard Model theory. Measurements from multiple Higgs boson decay channels are combined, enabling tighter constraints on a larger number of effective field theory parameters, and thereby reducing the parameter space for potential beyond-the-Standard Model physics. Ultimately, all results presented in this thesis are found to be consistent with the predictions of the Standard Model.