  In the preprint we present an outline of the one dimensional version of
topological Galois theory. The theory studies topological obstruction to
solvability of equations "in finite terms" (i.e. to their solvabilty by
radicals, by elementary functions, by quadratures and so on). The preprint is
based on the author's book on topological Galois theory. It contains
definitions, statements of results and comments to them. Basically no proofs
are presented.
  The preprint was 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.
}
