Algebraic renormalization

the long version

This book provides a pedagogical and self-contained introduction to the algebraic method of renormalization in perturbative quantum field theory. This method is based on general theorems of renormalization, in particular on the quantum action principle. It allows us to treat the problems of the renormalizability and the anomalies of models with local or global symmetries in terms of the algebraic properties of classical field polynomials. Several examples (e.g. topological models) are considered in some detail. One of the main advantages of this method, beyond its simplicity, is its great power, because no particular subtraction or regularization scheme preserving the symmetries of the problem is a priori required.