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The aim of this paper to introduce the reader to a recent point of view onthe Lipschitz classifications of complex singularities. It presents thecomplete classification of Lipschitz geometry of complex plane curvessingularities and in particular, it introduces the so-called bubble trick andbubble trick with jumps which are key tools to study Lipschitz geometry ofgerms. It describes also the thick-thin decomposition of a normal complexsurface singularity and built two geometric decompositions of a normal surfacegerm into standard pieces which are invariant by respectively inner and outerbilipschitz homeomorphisms. This leads in particular to the completeclassification of Lipschitz geometry for the inner metric.

An introduction to Lipschitz geometry of complex singularities