This book offers an overview of selected topics on the topology of
singularities, with emphasis on its relations to other branches of
geometry and topology. The opening chapters cover complex singularities
and collect a myriad of results spread in a vast literature, including
recent research. The second part of the book studies real analytic
singularities which arise from the topological and geometric study of
holomorphic vector fields and foliations. In the low dimensional case
these turn out to be related to fibred links in the 3-sphere defined by
meromorphic functions.