This volume is the proceedings of the workshop 'Singularities in Generic Geometry and Applications — Kobe-Kyoto 2015 (Valencia IV)' — which was held at Kobe University June 3-6 and RIMS, Kyoto University June 8-10, 2015.The workshop was the fourth in a sequence of biennial workshops, which had been started in Valencia (Spain, 2009).The volume consists fifteen original research articles and three survey articles by specialists in Singularity theory and its applications to Differential Topology and Differential Geometry. It is highly recommended to researchers and graduate students who are interested in these areas.Published by Mathematical Society of Japan and distributed by World Scientific Publishing Co. for all markets except North America