Since its discovery at the large hadron collider (LHC) in 2012, the Higgs boson and its properties are under intense investigation from both theorists and experimentalists. As the only scalar particle in the Standard Model (SM), the Higgs is believed to be closely related to the nature of electroweak symmetry breaking and the mass generation of fundamental massive particles. Respectively, they manifest as the couplings between Higgs to massive bosons (gauge couplings) and Higgs to fermions (Yukawa couplings). Thus, measurements of the Higgs sector properties are highly motivated either to confirm our current theory, the standard model, or to reveal possible new theories.
With the ongoing effort at the LHC, the Higgs is studied through various production and decay channels. However at a hadron collider, the large background and the ignorance of the partonic center of mass energy make testing many parameters of the Higgs sector challenging. For this dissertation I studied Higgs processes at a lepton collider, explored mass determination abilities for certain processes at a lepton collider and also studied the challenging Higgs decay to light jets at the LHC. These studies suggest new observables to improve our sensitivity to the Higgs sector and to constrain possible new physics deviations.