Abstarct: In this work electronic structure and optical properties of CeO2 in the bulk and nanosheetes were investigated theoritically. Structural and optical characteristics of bulk CeO2 introduce in chapter one. Density Functional Theory (DFT) and Quantom espresso software are presented in chapter 2. In chapters 3 and 4, the results of optical and electronic studies of the bulk and nanosheetes of CeO2, are presented which were calculated by using DFT respectivley. Ultrasoft Pseudoptential whit Quantom espresso software were used for all calculations. In optical studies, the band gap energy, density of states, dielectric functiones, absorbtion, optical conductivity, refractive index, extinction coefficient, energy lost and reflectivity were calculated for both bulk and nonosheets. The calculations were performed by both LDA and GGA aproximations. The obtained density of state of showed that the lower part of the conduction band (near the Fermi level), composes of the Ce: 4f states and the edge states of valance band contains O:2p. The result showed that the band gap calculated by the LDA approximation is closer to the experimental value than GGA approximation and the band gap energy of nanosheetes significaly descrease compared to the band gap of the bulk CeO2.