  We investigate the physics of the lightest CP-even MSSM Higgs boson at the
Tevatron, the LHC, a linear e+e- collider, a gamma gamma collider and a mu+mu-
collider. The analysis is performed in the three most prominent soft
SUSY-breaking scenarios, mSUGRA, mGMSB and mAMSB. For all colliders the
observability and parameter regions with suppressed production cross sections
(compared to a SM Higgs boson with the same mass) are investigated. For the
lepton and photon colliders the potential is analyzed of precision measurements
of the branching ratios of the light CP-even Higgs boson for obtaining indirect
bounds on the mass of the CP-odd Higgs boson and the high-energy parameters of
the soft SUSY-breaking scenarios. In regions of the parameter space where the
LHC can detect the heavy Higgs bosons, precision measurements of the properties
of the light Higgs boson at the linear collider can provide valuable
information for distinguishing between the mSUGRA, mGMSB and mAMSB scenarios.
