This paper presents a nonperturbative evolution equation for quantum gravity, derived from a scale-dependent effective action. The equation governs the renormalization group flow of the action and is invariant under general coordinate transformations. It satisfies modified BRS Ward identities and is used to study the behavior of Newton's constant and the cosmological constant in different dimensions. The evolution equation is solved for a simple truncation of the space of actions, and nonperturbative corrections to the beta function of Newton's constant are derived in 2+ε dimensions. In four dimensions, it is shown that Einstein gravity is "antiscreening," meaning Newton's constant increases at large distances. The paper also discusses the effective average action, its relation to the average action, and the derivation of the renormalization group equation. The evolution equation is formulated in terms of a background gauge fixing technique, and the cutoff operators are defined to discriminate between high- and low-momentum modes. The paper concludes with the derivation of modified Ward identities and the use of truncations to find approximate nonperturbative solutions. The results show that the evolution equation is well-defined even for non-positive definite actions and that the effective average action satisfies the usual Ward identities in the limit of a vanishing infrared cutoff. The paper also discusses the use of the Einstein-Hilbert truncation to study the renormalization group flow of the action in different dimensions.This paper presents a nonperturbative evolution equation for quantum gravity, derived from a scale-dependent effective action. The equation governs the renormalization group flow of the action and is invariant under general coordinate transformations. It satisfies modified BRS Ward identities and is used to study the behavior of Newton's constant and the cosmological constant in different dimensions. The evolution equation is solved for a simple truncation of the space of actions, and nonperturbative corrections to the beta function of Newton's constant are derived in 2+ε dimensions. In four dimensions, it is shown that Einstein gravity is "antiscreening," meaning Newton's constant increases at large distances. The paper also discusses the effective average action, its relation to the average action, and the derivation of the renormalization group equation. The evolution equation is formulated in terms of a background gauge fixing technique, and the cutoff operators are defined to discriminate between high- and low-momentum modes. The paper concludes with the derivation of modified Ward identities and the use of truncations to find approximate nonperturbative solutions. The results show that the evolution equation is well-defined even for non-positive definite actions and that the effective average action satisfies the usual Ward identities in the limit of a vanishing infrared cutoff. The paper also discusses the use of the Einstein-Hilbert truncation to study the renormalization group flow of the action in different dimensions.