  We discuss here the effect of band nesting and topology on the spectrum of
excitons in a single layer of MoS$_2$, a prototype transition metal
dichalcogenide material. We solve for the single particle states using the ab
initio based tight-binding model containing metal $d$ and sulfur $p$ orbitals.
The metal orbitals contribution evolving from $K$ to $\Gamma$ points results in
conduction-valence band nesting and a set of second minima at $Q$ points in the
conduction band. There are three $Q$ minima for each $K$ valley. We accurately
solve the Bethe-Salpeter equation including both $K$ and $Q$ points and obtain
ground and excited exciton states. We determine the effects of the
electron-hole single particle energies including band nesting, direct and
exchange screened Coulomb electron-hole interactions and resulting topological
magnetic moments on the exciton spectrum. The ability to control different
contributions combined with accurate calculations of the ground and excited
exciton states allows for the determination of the importance of different
contributions and a comparison with effective mass and $k\cdot p$ massive Dirac
fermion models.
