This volume, containing 32 papers on a broad range of topics of current interest in the field, is an outgrowth of the synergism of Discrete and Computational Geometry. It includes surveys and research articles exploring geometric arrangements, polytopes, packing, covering, discrete convexity, geometric algorithms and their complexity, and the combinatorial complexity of geometric objects, particularly in low dimension.There are points of contact with many applied areas such as mathematical programming, visibility problems, kinetic data structures, and biochemistry, and with algebraic topology, geometric probability, real algebraic geometry, and combinatorics.