Group VI elemental 2D materials have been predicted to possess promising properties in electronics, optoelectronics, thermoelectricity, sensors, and detectors[1–5]. In this thesis, we present the electronic and optical properties of square selenene (s-Se), a 2D allotrope of selenium. We start by calculating the electronic properties using Density Functional Theory (DFT). These ab initio calculations show the formation of an anisotropic cone with semi-Dirac dispersion in a non-symmetric point, denoted P1, in the Brillouin zone, which forms a narrow gap (∼0.1 eV) due to spin-orbit coupling (SOC). Then, we uncover an intricate reciprocal space spin texture along the Brillouin zone, with spin-momentum locking around P1. To conclude the DFT calculations, we show the existence of edge states in two types of s-Se nanoribbons, with one of them presenting topologically non-trivial features, which are confirmed in other works[1,6]. We then replicate a k⋅p Hamiltonian, for the band structure around P1, from the literature[1] and add various SOC terms to obtain an effective model that describes the band structure data from fully relativistic DFT calculations and qualitatively reproduces the spin texture in reciprocal space. Using this effective model, we describe the exciton formation in the Dirac-like cone gap using the variational method while considering an anisotropic version of the Rytova-Keldysh potential[7]. This analysis provides a first characterisation of the exciton ground-state in square selenene, describing its binding energy (Eb=-24 meV) and wavefunction, which, to the best of our knowledge, have not been previously reported.