  In this paper we present a paradigmatic tight-binding model for single-layer
as well as for multi-layered semiconducting MoS$_2$ and similar transition
metal dichalcogenides. We show that the electronic properties of multilayer
systems can be reproduced in terms of a tight-binding modelling of the
single-layer hopping terms by simply adding the proper interlayer hoppings
ruled by the chalcogenide atoms. We show that such tight-binding model permits
to understand and control in a natural way the transition between a direct-gap
band structure, in single-layer systems, to an indirect gap in multilayer
compounds in terms of a momentum/orbital selective interlayer splitting of the
relevant valence and conduction bands. The model represents also a suitable
playground to investigate in an analytical way strain and finite-size effects.
