The renormalization

This document gathers 6 articles. In the first article the author reviews the theory of perturbative renormalization, discusses its limitations and gives a brief introduction to the powerful point of view of the renormalization group, which is necessary to go beyond perturbation theory and to define renormalization in a constructive way. The second article is dedicated to renormalization group methods by illustrating them with examples. The third article describes the implementation of renormalization ideas in quantum field theory. The mathematical aspects of renormalization are given in the fourth article where the link between renormalization and the Riemann-Hilbert problem is highlighted. The fifth article gives an overview of the main features of the theoretical calculations that have been done in order to obtain accurate predictions for the anomalous magnetic moments of the electron and of the muon within the standard model. The challenge is to make theory match the unprecedented accuracy of the last experimental measurements. The last article presents how ''physics beyond the standard model'' will be revealed at the large hadron collider (LHC) at CERN. This accelerator will be the first to explore the 1 TeV energy range directly. Supersymmetry, extra-dimensions and Higgs boson will be the different challenges. It is not surprising that all theories put forward today to subtend the electro-weak breaking mechanism, predict measurable or even spectacular signals at LHC. (A.C.)