  1$T$-TaS$_2$ is the only insulating transition-metal dichalcogenide (TMD)
with an odd number of electrons per unit cell. This insulating state is
non-magnetic, making it a potential spin-liquid candidate. The unusual
electronic behavior arises from a naturally occurring nearly flat mini-band,
where the properties of the strongly correlated states are significantly
influenced by the microscopic starting point, necessitating a detailed and
careful investigation. We revisit the electronic band structure of
1$T$-TaS$_2$, starting with the tight-binding model without CDW order. Symmetry
dictates the nature of spin-orbit coupling (SOC), which, unlike in the 2H TMD
structure, allows for strong off-diagonal "spin-flip" terms as well as Ising
SOC. Incorporating the CDW phase, we construct a 78$\times$78 tight-binding
model to analyze the band structure as a function of various parameters. Our
findings show that an isolated flat band is a robust feature of this model.
Depending on parameters such as SOC strength and symmetry-allowed orbital
splittings, the flat band can exhibit non-trivial topological classifications.
These results have significant implications for the strongly correlated physics
emerging from interacting electrons in the half-filled or doped flat band.
