This volume contains the proceedings of the workshop Singularities in Generic Geometry and Applications-Kobe-Kyoto 2015 (Valencia IV), which was held at Kobe University from June 3-6, and the Research Institute for Mathematical Sciences (RIMS), Kyoto University, from June 8-10, 2015. The workshop was the fourth in a series of biennial workshops. The first workshop was in Valencia, Spain, in 2009.

The volume consists of 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 for researchers and graduate students who are interested in these areas.