  Usually, General Relativity (GR) is known to be unrenormalizable
perturbatively from the viewpoint of quantum field theory. But in the modern
sense of renormalizability, there still remains the possibility to investigate
whether GR is "nonpertubatively" renormalizable or not. Here I review the
basics and results in this topic based on the "Effective Average Action"
approach which was proposed by M.Reuter, and discuss its application to the
balck hole geometry.
