The relativistic band structure of thallium has been calculated using the linear muffin-tin orbital (LMTO) method. The positions and extents of the bands were found to follow the Wigner-Seitz rule approximately, and the origin of the dispersion of the bands was established from the canonical s and p bands for the HCP structure. Energy bands have been evaluated both with and without spin-orbit coupling which is particularly large in thallium. Energy bands close to the Fermi level were found to be mainly 6p like in character. The 6s states lay below the 6p bands and were separated from them by an energy gap. The 6d and 7s bands were found to be far above the Fermi level and the 5d states were found to be far below it. Fermi surface properties and the electronic specific heat are computed and compared with experiment. The joint density of states has also been computed and is in reasonable agreement with experimental optical properties.