In this thesis, I develop a theoretical overview of the optical and electronic prop- erties of ultrathin films of layered hexagonal Indium Selenide. The analysis is carried out using a combination of atomistic tight-binding and k Â· p approaches, with model parameters found using density functional theory calculations, corrected for the un- derestimation of the band gap which would otherwise have substantial effects on the properties of the system. A tight-binding model for monolayer and few-layer Indium Selenide is developed. The model is used to explore the behaviour of the few-layer bands of InSe, showing a significant reduction in the gap for thicker crystals due to relatively strong electronic coupling (i.e. tight-binding hops) between the layers. Oscillator strengths generated by the model are used to describe the dominant polarisation character and strength of interband optical transitions, with the principal interband transition coupling pri- marily to out-of-plane polarised light. Taking advantage of the anisotropy of Indium Selenide we use the results of the tight-binding model to guide the development of a âhybrid k Â· p tight-bindingâ model, in which the individual constituent monolayers are described in a band-basis k Â· p picture, while the relatively strong electronic coupling between the layers is described in a language of tight-binding hops between the monolayer bands. We use this model to describe the bands and gaps of both aligned crystals and misaligned laminate films of InSe, the latter of which exhibit increased band gaps due to reduced electronic coupling between misaligned layers. The model is applied self-consistently to the question of intersubband optical transitions involving electrons in gate-doped films. Since the band edges in Indium Selenide appear in the vicinity of the (in-plane) Î-point, spin-orbit coupling does not give rise to spin-splitting at the band edges in the same manner as in, for example, the transition metal dichalcogenides. Interband mixing induced by spin-orbit coupling does however have important consequences for the polarisation of optical transitions. We analyse this effect, which is strongest in the monolayer, both using the hybrid k Â· p tight-binding model, and by adding atomic spin- orbit coupling to the fully atomistic tight-binding approach. The spin-orbit splitting in the conduction band of few-layer Indium Selenide is found to be of the Rashba type, and we show how the strength of the Rashba splitting will depend on the interplay between the symmetry-breaking of the crystal structure itself, and that provided by the electric field of gates used to dope the system. We compare the predictions of the model with magnetotransport experiments showing evidence of weak antilocalisation.