  We present a systematic description of the mathematical techniques for
studying multiloop Feynman diagrams which constitutes a full-fledged and
inherently more powerful alternative to the BPHZ theory. The new techniques
emerged as a formalization of the reasoning behind a recent series of record
multiloop calculations in perturbative quantum field theory. It is based on a
systematic use of the ideas and notions of the distribution theory. We identify
the problem of asymptotic expansion of products of singular functions in the
sense of distributions as a key problem of the theory of asymptotic expansions
of multiloop Feynman diagrams. Its complete solution for the case of Euclidean
Feynman diagrams (the so-called Euclidean asymptotic operation for products of
singular functions) is explicitly constructed and studied.
