Singularities and Their Interaction with Geometry and Low Dimensional TopologyThe book is a collection of surveys and original research articles concentrating on new perspectives and research directions at the crossroads of algebraic geometry, topology, and singularity theory. The papers, written by leading researchers working on various topics of the above fields, are the outcome of the Nmethi60: Geometry and Topology of Singularities conference held at the Alfrd Rnyi Institute of Mathematics in Budapest, from May 27 to 31,