  We carry out a detailed theoretical study of the electronic and optical
properties of bulk and monolayer bismuth triiodide (BiI$_{3}$), a layered metal
halide, using the ab initio GW+BSE scheme with a full spinorial formulation. We
discuss in detail the effects due to the change of dimensionality and the role
of spin-orbit coupling. Moreover, we compute the exciton dispersion by solving
the BSE at finite momentum, also analysing transverse (TE) and longitudinal
(LE) excitons, and the L-T splitting at $\bf{q}\approx\Gamma$. The results
provide a reference for future experimental measurements. In addition, the
interplay between spin-orbit coupling and large binding energy, together with
the role of quantum confinement, confirm that BiI$_{3}$ is an interesting
material for opto-electronic applications and show that it is a good candidate
for the study of exciton dynamics.
