I want to recommend the following paper to anyone who wants the spec up on Renormalization Group flows, fixed points, or asymptotic safety. The author is interested in reviving the functinal integral approach to QG, which was aboandoned when 't Hooft and Veltzman showed GR was nonrenomalizable in the 1970s, in the context of the possible asymptotic safety of GR. In the course of his discussion of the issues involved he gives a mini tutorial in the topics I listed above. Here is the "contact information" for the paper: http://arxiv.org/PS_cache/gr-qc/pdf/0610/0610018.pdf [Broken] The Asymptotic Safety Scenario in Quantum Gravity – An Introduction – M. Niedermaier∗ Comments: 72p, 1 figure. Introduction to the subject based on several talks and conference contributions. An elaboration on the evidence (c) and (d) (see abstract) can be found in a forthcoming `Living Reviews in Relativity' article with M. Reuter The asymptotic safety scenario in quantum gravity is reviewed, according to which a renormalizable quantum theory of the gravitational field is feasible which reconciles asymptotically safe couplings with unitarity.All presently known evidence is surveyed: (a) from the 2+\epsilon expansion,(b) from renormalizable higher derivative gravity theories and a `large N' expansion in the number of matter fields, (c) from the 2-Killing vector reduction, and (d) from truncated flow equations for the effective average action. Special emphasis is given to the role of perturbation theory as a guide to `asymptotic safety'. Further it is argued that as a consequence of the scenario the selfinteractions appear two-dimensional in the extreme ultraviolet. Two appendices discuss the distinct roles of the ultraviolet renormalization in perturbation theory and in the flow equation formalism.