Ab initio, electronic energy bands of MoS2 single layer are reported within the local density functional approximation. The inclusion of spin orbit coupling reveals the presence of two excitons A and B. We also discuss the change of physical properties of MoS2 from multilayer and bulk counterparts. The nature of the band gap changes from indirect to direct when the thickness is reduced to a single monolayer. The imaginary and real dielectric functions are investigated. Refractive index and birefringence are also reported. The results suggest that MoS2 is suitable for potential applications in optoelectronic and photovoltaic devices. The ab initio study is essential to propose the crucial parameters for the analytical model used for A-B exciton properties of the monolayer MoS2. From a theoretical point of view, we consider how the exciton behavior evolves under environmental dielectrics.