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This thesis provides the first comprehensive theoretical overview of the electronic and optical properties of two dimensional (2D) Indium Selenide: atomically thin films of InSe ranging from monolayers to few layers in thickness. The thesis shows how the electronic propertes of 2D InSe vary significantly with film thickness, changing from a weakly indirect semiconductor for the monolayer to a direct gap material in the bulk form, with a strong band gap variation with film thickness predicted and recently observed in optical experiments. The proposed theory is based on a specially designed hybrid k.p tight-binding model approach (HkpTB), which uses an intralayer k.p Hamiltonian to describe the InSe monolayer, and tight-binding-like interlayer hopping. Electronic and optical absorption spectra are determined, and a detailed description of subbands of electrons in few-layer films and the influence of spin-orbit coupling is provided. The author shows that the principal optical excitations of InSe films with the thickness from 1 to 15 layers broadly cover the visible spectrum, with the possibility of extending optical functionality into the infrared and THz range using intersubband transitions.