  K\"ahler's paper "\"Uber die Verzweigung einer algebraischen Funktion zweier
Ver\"anderlichen in der Umgebung einer singul\"aren Stelle" offered a more
perceptual view of the link of a complex plane curve singularity than that
provided shortly before by Brauner. K\"ahler's innovation of using a "square
sphere" became standard in the toolkit of later researchers on singularities.
We describe his contribution and survey developments since then, including a
brief discussion of the topology of isolated hypersurface singularities in
higher dimension.
