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Classifying the symmetries of the scalar sector in multi-Higgs-doublet modelsis the main focus of this thesis. We have found certain symmetries that arealways broken in models with more than two doublets, which we name "frustratedsymmetries". In the attempt towards the classification of possible symmetriesin the scalar sector of the NHDM, we find that these symmetry groups are eithersubgroups of the maximal torus, or certain finite Abelian groups which are notsubgroups of maximal tori. For the subgroups of the maximal torus, we presentan algorithmic strategy that gives the full list of possible realizable Abeliansymmetries for any given $N$. We extend this strategy to include Abelianantiunitary symmetries (with generalized CP transformations) in NHDM. We alsoshow that multi-Higgs-doublet models can naturally accommodate scalar darkmatter candidates protected by the group $\Z_p$, since these groups arerealizable in NHDM. These models do not require any significant fine-tuning andcan lead to a variety of forms of microscopic dynamics among the dark mattercandidates.

Symmetries of the Scalar Sector of Multi-Higgs-Doublet Models