  We present algorithms for parametrizing by radicals an irreducible curve, not
necessarily plane, when the genus is less o equal to 4 and they are defined
over an algebraically closed field of characteristic zero. In addition, we also
present an algorithm for parametrizing by radicals any irreducible plane curve
of degree $d$ having at least a point of multiplicity $d-r$, with $1\leq r \leq
4$ and, as a consequence, every irreducible plane curve of degree $d \leq 5$
and every irreducible singular plane curve of degree 6.
