The paper introduces a scale-dependent effective action for gravity and derives an exact nonperturbative evolution equation that governs its renormalization group flow. This equation is invariant under general coordinate transformations and satisfies modified BRS Ward-Identities. The evolution equation is solved for a simple truncation of the space of actions, leading to nonperturbative corrections to the β-function of Newton's constant in 2+ε dimensions and investigating its dependence on the cosmological constant in 4 dimensions. In 4 dimensions, Einstein gravity is found to be "antiscreening," meaning that Newton's constant increases at large distances. The paper also discusses the background gauge technique, which is used to make the effective action invariant under general coordinate transformations, and the construction of the effective action parallels the definition of the "effective average action" used in other theoretical contexts.The paper introduces a scale-dependent effective action for gravity and derives an exact nonperturbative evolution equation that governs its renormalization group flow. This equation is invariant under general coordinate transformations and satisfies modified BRS Ward-Identities. The evolution equation is solved for a simple truncation of the space of actions, leading to nonperturbative corrections to the β-function of Newton's constant in 2+ε dimensions and investigating its dependence on the cosmological constant in 4 dimensions. In 4 dimensions, Einstein gravity is found to be "antiscreening," meaning that Newton's constant increases at large distances. The paper also discusses the background gauge technique, which is used to make the effective action invariant under general coordinate transformations, and the construction of the effective action parallels the definition of the "effective average action" used in other theoretical contexts.