This paper presents the discovery of the quantum spin Hall (QSH) effect in graphene, a two-dimensional material with a honeycomb lattice of carbon atoms. The study shows that spin-orbit (SO) interactions can convert graphene from a semimetallic state to a QSH insulator, characterized by a bulk energy gap and gapless edge states that support spin and charge transport. These edge states are non-chiral and robust against disorder due to their spin-dependent directionality. The QSH effect in graphene is distinct from the spin Hall effect in three-dimensional systems and resembles the quantum Hall effect, with spin and charge currents transported in gapless edge states. The SO interaction in graphene leads to a new term in the Hamiltonian, which is symmetric under parity and time reversal. This term generates a gap in the electronic structure, and when combined with a Rashba term (arising from a perpendicular electric field or substrate interaction), the gap remains finite. The QSH state in graphene is topologically distinct from a simple insulator, with opposite signs of the energy gap at the K and K' points in the Brillouin zone. This leads to a quantized spin Hall conductivity, $ \sigma_{xy}^{s} = e/(2\pi) $, which is robust against weak interactions and disorder. The edge states in graphene are spin-filtered, with electrons of opposite spin propagating in opposite directions. These states are protected by time reversal symmetry and are robust against backscattering. The QSH effect in graphene can be observed through low-temperature charge transport and spin injection experiments. The study also estimates the magnitude of the SO interaction in graphene, finding that it is comparable to known SO splittings in graphite. The SO interaction is further renormalized by long-range Coulomb interactions, leading to a larger energy gap. The QSH effect in graphene represents a new class of spin Hall insulator and may provide a foundation for searching for similar effects in other two-dimensional or layered materials.This paper presents the discovery of the quantum spin Hall (QSH) effect in graphene, a two-dimensional material with a honeycomb lattice of carbon atoms. The study shows that spin-orbit (SO) interactions can convert graphene from a semimetallic state to a QSH insulator, characterized by a bulk energy gap and gapless edge states that support spin and charge transport. These edge states are non-chiral and robust against disorder due to their spin-dependent directionality. The QSH effect in graphene is distinct from the spin Hall effect in three-dimensional systems and resembles the quantum Hall effect, with spin and charge currents transported in gapless edge states. The SO interaction in graphene leads to a new term in the Hamiltonian, which is symmetric under parity and time reversal. This term generates a gap in the electronic structure, and when combined with a Rashba term (arising from a perpendicular electric field or substrate interaction), the gap remains finite. The QSH state in graphene is topologically distinct from a simple insulator, with opposite signs of the energy gap at the K and K' points in the Brillouin zone. This leads to a quantized spin Hall conductivity, $ \sigma_{xy}^{s} = e/(2\pi) $, which is robust against weak interactions and disorder. The edge states in graphene are spin-filtered, with electrons of opposite spin propagating in opposite directions. These states are protected by time reversal symmetry and are robust against backscattering. The QSH effect in graphene can be observed through low-temperature charge transport and spin injection experiments. The study also estimates the magnitude of the SO interaction in graphene, finding that it is comparable to known SO splittings in graphite. The SO interaction is further renormalized by long-range Coulomb interactions, leading to a larger energy gap. The QSH effect in graphene represents a new class of spin Hall insulator and may provide a foundation for searching for similar effects in other two-dimensional or layered materials.