This volume contains 17 surveys that cover many recent developments in Discrete Geometry and related fields. Besides presenting the state-of-the-art of classical research subjects like packing and covering, it also offers an introduction to new topological, algebraic and computational methods in this very active research field. The readers will find a variety of modern topics and many fascinating open problems that may serve as starting points for research.

Introduction.- A. Barvinok: The tensorization trick in geometry.- K. Bezdek and M. A. Khan: Contact numbers for sphere packings.- P. M. Blagojević, A. S. D. Blagojević, and G. M. Ziegler: The topological Tverberg theorem plus constraints.- B. Csikós: On the volume of Boolean expressions of balls – A review of the Kneser-Poulsen conjecture.- F. de Zeeuw: A survey of Elekes-Rónyai-type problems.- G. Domokos and G. W. Gibbons: The geometry of abrasion.- F. M. de Oliveira Filho and F. Vallentin: Computing upper bounds for the packing density of congruent copies of a convex body.- P. Hajnal and E. Szemerédi: Two geometrical applications of the semi-random method.- A. F. Holmsen: Erdős-Szekeres theorems for families of convex sets.- R. Kusner, W. Kusner, J. C. Lagarias, and S. Shlosman: Configuration spaces of equal spheres touching a given sphere: the twelve spheres problem.- E. León and G. M. Ziegler: Spaces of convex n-partitions.- P. McMullen: New regular compounds of 4-polytopes.- O.R. Musin, Five Essays on the Geometry of László Fejes Tóth.- M. Naszódi: Flavors of translative coverings.- M. Sharir and Noam Solomon: Incidences between points and lines in three dimensions.- J. Solymosi and F. de Zeeuw: Incidence bounds for complex algebraic curves on Cartesian products.- K. J. Swanepoel: Combinatorial distance geometry in normed spaces.