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The paper is an introduction to the use of the classical Newton-Puiseuxprocedure, oriented to an algorithmic description of it. This procedure enablesto get polynomial approximations for parameterizations of branches of analgebraic plane curve at a singular point. We look for an approach that can beeasily grasped and almost self contained. We illustrate the use of thealgorithm, first in a completely worked out example of a curve with a point ofmultiplicity 6, and secondly in the study of triple points on reduced planecurves.

Newton-Puiseux algorithm and triple points for planes curves