Theory of asymptotic operation. A summary of basic principles

This summary of several talks given in 1990-1993 discusses the problem of asymptotic expansions of multiloop Feynman diagrams in masses and external momenta - a central problem in perturbative quantum field theory. Basic principles of the theory of asymptotic operation -- the most powerful tool for that purpose -- are discussed. Its connection with the conventional methods is explained (the BPHZ theory, the method of leading logarithmic approximation etc.). The problem of non-euclidean asymptotic regimes is discussed as well as ways of its solution.