  This preprint is dedicated to a self contained simple proof of the classical
criteria for representability of algebraic functions of several complex
variables by radicals. It also contains a criteria for representability of
algebroidal functions by composition of single-valued analytic functions and
radicals, and a result related to the 13-th Hilbert problem. This preprint is
an extended version of the author's 1971 paper. It is written as a part of the
comments to a new edition (in preparation) of the classical book `Integration
in finite terms' by J.F.~Ritt.
