  We derive the one-loop beta functions for a theory of gravity with generic
action containing up to four derivatives. The calculation is done in arbitrary
dimension and on an arbitrary background. The special cases of three, four,
near four, five and six dimensions are discussed in some detail. We find that
the theories have nontrivial UV fixed points and are asymptotically safe in all
dimensions we study. We also find an indication that Weyl-invariant fixed point
exists in four dimensions. The new massive gravity in three dimensions does not
correspond to any fixed point.
