This paper presents a theoretical study of the dielectric function, screening, and plasmons in two-dimensional (2D) graphene. The dynamical dielectric function, ε(q, ω), is calculated using the self-consistent field approximation (RPA). The results are used to determine the dispersion of the plasmon mode and the electrostatic screening of the Coulomb interaction in 2D graphene. The plasmon dispersion at long wavelengths (q → 0) shows a local classical behavior, ω_cl = ω₀√q, but the density dependence of the plasma frequency is different from that of conventional 2D electron systems. The wave vector-dependent plasmon dispersion and static screening function exhibit different behavior compared to the usual 2D case. The intrinsic interband contributions to static graphene screening can be effectively absorbed in a background dielectric constant. The electron dynamics in 2D graphene are modeled by a chiral Dirac equation, which describes a linear relation between energy and momentum. The corresponding kinetic energy for 2D wave vector k is given by ε_sk = sγ|k|, where s = ±1 indicates the conduction and valence bands, respectively. The density of states (DOS) is given by D(ε) = g_s g_v |ε|/(2πγ²), where g_s and g_v are the spin and valley degeneracies. The Fermi momentum and energy are given by k_F = (4πn/g_s g_v)^{1/2} and E_F = γ k_F, where n is the 2D carrier density. The polarizability is calculated using the RPA, and the results show that the plasmon dispersion for single-layer and bilayer graphene differs from conventional 2D systems. The plasmon dispersion for single-layer graphene is ω_cl ≡ ω_p(q→0) = ω₀√q, where ω₀ is proportional to n^{1/4}, while for bilayer graphene, the plasmon dispersion is ω_+ ≈ ω₀√(2q) and ω_- ≈ 2ω₀√d q, where d is the layer separation. The static screening function is calculated and found to be different from conventional 2D systems, with the screening wave vector proportional to the square root of the density. The static polarizability is calculated and found to be constant at q ≤ 2k_F, and increases linearly with q for q > 2k_F due to interband transitions. The effective dielectric constant in graphene is enhanced due to interband contributions, leading to a larger screening effect. The intrinsic screening contribution from interband transitions can be absorbed in the effective background lattice dielectric constant, allowing the use of the free carrier screening function for describing free carrier screening properties of 2D graphene. The results show that theThis paper presents a theoretical study of the dielectric function, screening, and plasmons in two-dimensional (2D) graphene. The dynamical dielectric function, ε(q, ω), is calculated using the self-consistent field approximation (RPA). The results are used to determine the dispersion of the plasmon mode and the electrostatic screening of the Coulomb interaction in 2D graphene. The plasmon dispersion at long wavelengths (q → 0) shows a local classical behavior, ω_cl = ω₀√q, but the density dependence of the plasma frequency is different from that of conventional 2D electron systems. The wave vector-dependent plasmon dispersion and static screening function exhibit different behavior compared to the usual 2D case. The intrinsic interband contributions to static graphene screening can be effectively absorbed in a background dielectric constant. The electron dynamics in 2D graphene are modeled by a chiral Dirac equation, which describes a linear relation between energy and momentum. The corresponding kinetic energy for 2D wave vector k is given by ε_sk = sγ|k|, where s = ±1 indicates the conduction and valence bands, respectively. The density of states (DOS) is given by D(ε) = g_s g_v |ε|/(2πγ²), where g_s and g_v are the spin and valley degeneracies. The Fermi momentum and energy are given by k_F = (4πn/g_s g_v)^{1/2} and E_F = γ k_F, where n is the 2D carrier density. The polarizability is calculated using the RPA, and the results show that the plasmon dispersion for single-layer and bilayer graphene differs from conventional 2D systems. The plasmon dispersion for single-layer graphene is ω_cl ≡ ω_p(q→0) = ω₀√q, where ω₀ is proportional to n^{1/4}, while for bilayer graphene, the plasmon dispersion is ω_+ ≈ ω₀√(2q) and ω_- ≈ 2ω₀√d q, where d is the layer separation. The static screening function is calculated and found to be different from conventional 2D systems, with the screening wave vector proportional to the square root of the density. The static polarizability is calculated and found to be constant at q ≤ 2k_F, and increases linearly with q for q > 2k_F due to interband transitions. The effective dielectric constant in graphene is enhanced due to interband contributions, leading to a larger screening effect. The intrinsic screening contribution from interband transitions can be absorbed in the effective background lattice dielectric constant, allowing the use of the free carrier screening function for describing free carrier screening properties of 2D graphene. The results show that the