During past few years, after successful isolation of graphen, a significant part of the researches were focused on investigation of the unique properties of 2D materials. One of the most recent groups of these materials is monoelemental 2D materials which are highly regarded for their high charge carrier mobility, appropriate size and adjustable band gap and especially the remarkable anisotropy in many of their properties. Arsenene is a member of this group that some of its monolayer and nanoribbons properties have been studied in this thesis based on density functional theory. The band structure changes of nanoribbons with respect to its width changes have been investigated from the view of quantum confinement effects. The results show that in hydrogen passivated arsenene nanoribbons, diverse effects of quantum confinement on different parts of valance and conduction bands are responsible for indirect-direct band gap transition and vice versa as reduction of the width. Electric conductivity of arsenene monolayer has been studied by calculation of charge carrier mobility and quantum traort. Calculations of mobility were performed for perfect crystalline structures without impurities and only the effects of phonon scattering are considered using Takagi formula. In our approach, the exact values of some parameters (especially mobility) are not desired and we focused on anisotropy in the calculated parameters in armchair and zigzag directions. The results show remarkable anisotropic conductivity in armchair and zigzag directions. Further calculations indicate that uniaxial strain in armchair and zigzag directions could intesivly affect anisotropic properties of arsenene monolayer which is due to very different properties of near fermi bands. Also, there is a very high difference between electron and hole mobility in armchair direction that could be useful for electron and hole separation purposes.