In this research, the electronic and optical properties of cerium dioxide (CeO2) were investigated by employing the pseudopotential method within the framework of density functional theory and using the Quantum ESPRESSO computational code under charge conservation, and within the two exchange-correlation approximations of LDA and GGA. In the first stage, the structure of cerium dioxide was simulated, and then the structural optimization and precise calculation of the properties of this compound were performed. In the section on electronic properties, the obtained results were compared with the data reported in previous studies, and it was demonstrated that the Local Density Approximation (LDA) has the closest agreement with the experimental and theoretical values. The band gap, band structure, and density of states were calculated and analyzed. The LDA approximation showed the band gap value to be 2.5 eV, whereas the Generalized Gradient Approximation (GGA), due to the overlap of energy levels with the Fermi level, was not able to determine the band gap precisely and did not present a specific gap. In the part of optical properties, the real and imaginary parts of the dielectric function were investigated, and based on them, the extinction, refraction, and reflection coefficients were extracted. Also, the energy loss spectrum was determined, which showed the optical gap of this compound to be 2.7 eV.