  Transition metal dichalcogenides (TMDCs) have emerged as a new two
dimensional materials field since the monolayer and few-layer limits show
different properties when compared to each other and to their respective bulk
materials. For example, in some cases when the bulk material is exfoliated down
to a monolayer, an indirect-to-direct band gap in the visible range is
observed. The number of layers $N$ ($N$ even or odd) drives changes in space
group symmetry that are reflected in the optical properties. The understanding
of the space group symmetry as a function of the number of layers is therefore
important for the correct interpretation of the experimental data. Here we
present a thorough group theory study of the symmetry aspects relevant to
optical and spectroscopic analysis, for the most common polytypes of TMDCs,
i.e. $2Ha$, $2Hc$ and $1T$, as a function of the number of layers. Real space
symmetries, the group of the wave vectors, the relevance of inversion symmetry,
irreducible representations of the vibrational modes, optical selection rules
and Raman tensors are discussed.
