The optical properties of graphene are analyzed as a function of frequency, temperature, and carrier density. The optical properties are determined by direct interband electron transitions. At low temperatures, the real part of the dynamic conductivity in doped graphene is a constant, while the imaginary part is logarithmically divergent at the threshold of interband transitions. The conductivity is derived from the Fermi-Dirac distribution and depends on the frequency and wave vector. For high frequencies, the dynamical conductivity is given by an expression involving the Fermi function and the chemical potential. The interband contribution dominates at low frequencies, while the intraband contribution is significant at higher frequencies. The conductivity is calculated using the dynamic conductivity and boundary conditions at interfaces. The reflectance and transmittance of graphene are studied, showing that the transmittance is proportional to the dimensionless parameter e²max(T, μ)/ħcω. At higher frequencies, the transmittance is controlled by the fine structure constant e²/ħc. The reflectance increases with temperature due to increased carrier density. The spectroscopy of graphene multilayers is also studied, showing that the transmittance and reflectance have maxima and minima due to interband absorption. The results show that the optical properties of graphene are determined by the interband transitions and the carrier density. The study provides a detailed microscopic theory of the optical properties of graphene monolayers and multilayers.The optical properties of graphene are analyzed as a function of frequency, temperature, and carrier density. The optical properties are determined by direct interband electron transitions. At low temperatures, the real part of the dynamic conductivity in doped graphene is a constant, while the imaginary part is logarithmically divergent at the threshold of interband transitions. The conductivity is derived from the Fermi-Dirac distribution and depends on the frequency and wave vector. For high frequencies, the dynamical conductivity is given by an expression involving the Fermi function and the chemical potential. The interband contribution dominates at low frequencies, while the intraband contribution is significant at higher frequencies. The conductivity is calculated using the dynamic conductivity and boundary conditions at interfaces. The reflectance and transmittance of graphene are studied, showing that the transmittance is proportional to the dimensionless parameter e²max(T, μ)/ħcω. At higher frequencies, the transmittance is controlled by the fine structure constant e²/ħc. The reflectance increases with temperature due to increased carrier density. The spectroscopy of graphene multilayers is also studied, showing that the transmittance and reflectance have maxima and minima due to interband absorption. The results show that the optical properties of graphene are determined by the interband transitions and the carrier density. The study provides a detailed microscopic theory of the optical properties of graphene monolayers and multilayers.