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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≤ r ≤ 4 and, as a consequence, every irreducible plane curve of degree d ≤ 5 and every irreducible singular plane curve of degree 6.doi:10.1016/j.jsc.2011.05.005 fatcat:gwrgtnnaqzfatj6f6xkhqvzn2q