  In this paper we consider the problem of finding explicitly canonical ideals
of one-dimensional Cohen-Macaulay local rings. We show that Gorenstein ideals
contained in a high power of the maximal ideal are canonical ideals. In the
codimension two case, from a Hilbert-Burch resolution, we show how to construct
canonical ideals of curve singularities. Finally, we translate the problem of
the analytic classification of curve singularities to the classification of
local Artin Gorenstein rings with suitable length.
