This volume contains the proceedings of the Institute for Mathematics and its Applications Participating Institutions Conference on Singularities, held at the University of Iowa in July 1986. The conference brought together an international group of researchers in algebraic and analytic singularity theory. This collection consists of research papers related to talks given at the conference. The field of singularities takes techniques from and gives results to many areas of mathematics, including algebraic and differential geometry and topology, complex analysis, Lie algebras and reflection groups, and combinatorics. All these areas are represented here with an emphasis on local algebraic, analytic and tangential properties, deformation and topology of singularities, and arrangements of hyperplanes.