  This thesis presents a theoretical analysis of the properties of the Higgs
bosons in the Standard Model (SM) and the minimal supersymmetric extension
(MSSM), which can be investigated at the LHC and $e^+e^-$ linear colliders. The
final goal is the reconstruction of the Higgs potential and thus the
verification of the Higgs mechanism. MSSM Higgs boson production processes at
future $\gamma\gamma$ colliders are calculated in several decay channels. Heavy
scalar and pseudoscalar Higgs bosons can be discovered in the $b\bar{b}$ final
state in the investigated mass range 200 to 800 GeV for moderate and large
values of $\tan\beta$. The $\tau^+\tau^-$ channel provides a heavy Higgs boson
discovery potential for large values of $\tan\beta$. Several mechanisms that
can be exploited at $e^+e^-$ linear colliders for the measurement of the
lifetime of a SM Higgs boson in the intermediate mass range are analysed. In
the $WW$ mode, the lifetime of Higgs scalars with masses below $\sim 160$ GeV
can be determined with an error less than 10%. The reconstruction of the Higgs
potential requires the measurement of the Higgs self-couplings. The SM and MSSM
trilinear Higgs self-couplings are accessible in double and triple Higgs
production. A theoretical analysis is presented in the relevant channels at the
LHC and $e^+e^-$ linear colliders. For high luminosities, the SM trilinear
Higgs self-coupling can be measured with an accuracy of 20% at a 500 GeV
$e^+e^-$ linear collider. The MSSM coupling among three light Higgs bosons has
to be extracted from continuum production. The other trilinear Higgs couplings
are measurable in a restricted range of the MSSM parameter space. At the LHC,
the $Hhh$ coupling can be probed in resonant decays.
