This report reviews the properties of Higgs bosons in the Standard Model (SM)
and its various extensions. We give an extensive overview about the potential
of the ILC operated at centre-of-mass energies up to 1 TeV (including the gamma
gamma option) for the determination of the Higgs boson properties. This
comprises the measurement of the Higgs boson mass, its couplings to SM fermions
and gauge bosons, and the determination of the spin and the CP quantum numbers
of the Higgs. The extensions of the SM that are analyzed in more detail are
heavy SM-like Higgs bosons, heavy Higgs bosons in the framework of
Supersymmetry (SUSY) and further exotic scenarios. We review recent theoretical
developments in the field of Higgs boson physics. The important question what
the ILC can contribute to Higgs boson physics after the LHC, the LHC/ILC
interplay and synergy is discussed. The impact of Higgs boson physics on
cosmology in several SUSY frameworks is analyzed. The impact of the accelerator
and dector performance on the precision of measurements are discussed in
detail. We propose a strategy to optimize future analyses. Open questions
arising for the various topics are listed, further topics of study and
corresponding roadmaps are suggested.Comment: 128 pages, lots of figures. One subsection added and other minor
modification