Introduction and plan of the notes

The topic is broad and complex. Even focusing on a particular aspect would take a whole monograph, and indeed there are several dedicated to this purpose. Here the focus is on the relatively new approach of Functional Renormalization Group Equations (FRGE, sometimes called, misleadingly in our opinion, “exact”), and in particular on Wetterich’s equation, which is being widely applied in statistical Physics, Standard Model Physics, and to study the asymptotic safety conjecture of Weinberg for Quantum Gravity.