This volume offers the opportunity to establish the state of the art and to present new trends, new ideas and new results in all of the branches of singularities - reflected by the contributions in this book: equisingularity of sets and mappings, geometry of singular complex analytic sets, singularities of mappings, characteristic classes, classification of singularities, interaction of singularity theory with some of the new ideas in algebraic geometry imported from theoretical physics, applications of singularity theory to geometry of surfaces in low dimensional euclidean spaces, to differential equations and to bifurcation theory.