Renormalization: an advanced overview

Abstract: We present several approaches to renormalization in QFT: the multi-scale analysis in perturbative renormalization, the functional methods `a la Wetterich equation, and the loop-vertex expansion in non-perturbative renormalization. While each of these is quite well-established, they go beyond standard QFT textbook material, and may be little-known to specialists of each other approach. This review is aimed at bridging this gap.