The book of the famous theoretical physicist O. Steinman is devoted to the formulation of the perturbation method in axiomatic field theory. Its advantage is the combination of mathematical rigor of presentation with a clear understanding of the physical essence of the problem. Many of the results belong to the author himself. The mathematical apparatus of the monograph is based on the Glaser-Lehman-Zimmerman equation system for delayed Green functions. Its main part is devoted to the study of the properties of the expansions of these functions by the coupling constant. Particular attention is paid to the description of the behavior of the obtained solutions at short distances. The monograph ends with an analysis of the renormalizability problem of field theory, which plays an important role in elementary particle physics. The book is of interest to theoretical physicists - scientists, students and graduate students, as well as mathematicians interested in mathematical problems of quantum field theory.