Thirty Essays on Geometric Graph Theory In many applications of graph theory graphs are regarded as geometric objects drawn in the plane or in some other surface. The traditional methods of abstract graph theory are often incapable of providing satisfactory answers to questions arising in such applications. In the past couple of decades many powerful new combinatorial and topological techniques have been developed to tackle these problems. Today geometric graph theory is a burgeoning field with many striking results and appealing open questions. This contributed volume contains thirty original survey and research papers on important recent developments in geometric graph theory. The contributions were thoroughly reviewed and written by excellent researchers in this field. Introduction 1) B. Ábrego S. Fernández Merchant G. Salazar: The rectilinear crossing number of K_n: closing in (or are we) 2) E. Ackerman: The maximum number of tangencies among convex regions with a triangle free intersection graph 3) G. Aloupis B. Ballinger S. Collette S. Langerman A. Pór D.R.Wood: Blocking coloured point sets 4) M. Al Jubeh G. Barequet M. Ishaque D. Souvaine Cs. D. Tóth A. Winslow: Constrained tri connected planar straight line graphs 5) S. Buzaglo R. Pinchasi G. Rote: Topological hypergraphs 6) J. Cano Vila L. F. Barba J. Urrutia T. Sakai: On edge disjoint empty triangles of point sets 7) J. Cibulka J. Kynčl V. Mészáros R. Stolař P. Valtr: Universal sets for straight line embeddings of bicolored graphs 8) G. Di Battista F. Frati: Drawing trees outerplanar graphs series parallel graphs and planar graphs in small area 9) W. Didimo G. Liotta: The crossing angle resolution in graph drawing 10) A. Dumitrescu: Mover problems 11) S. Felsner: Rectangle and square representations of planar graphs 12) R. Fulek N. Saeedi D. Sariöz: Convex obstacle numbers of outerplanar graphs and bipartite permutation graphs 13) R. Fulek M. Pelsmajer M. Schaefer D. Štefankovič: Hanani Tutte monotone drawings and level planarity 14) R. Fulek A. Suk: On disjoint crossing families in geometric graphs 15) M. Hoffmann A. Schulz M. Sharir A. Sheffer Cs. D. Tóth E. Welzl: Counting plane graphs: flippability and its applications 16) F. Hurtado Cs. D. Tóth: Geometric graph augmentation: a generic perspective 17) M. Kano K. Suzuki: Discrete geometry on red and blue points in the plane lattice 18) Gy. Károlyi: Ramsey type problems for geometric graphs 19) Ch. Keller M. Perles E. Rivera Campo V. Urrutia Galicia: Blockers for non crossing spanning trees in complete geometric graphs 20) A. V. Kostochka K. G. Milans: Coloring clean and K_4 free circle graphs 21) F. Morić D. Pritchard: Counting large distances in convex polygons: a computational approach 22) A. Raigorodskii: Coloring distance graphs and graphs of diameters 23) M. Schaefer: Realizability of graphs and linkages 24) C. Smyth: Equilateral sets in l_dp 25) A. Suk: A note on geometric 3 hypergraphs 26) K. Swanepoel: Favourite distances in high dimensions 27) M. Tancer: Intersection patterns of convex sets via simplicial complexes a survey 28) G. Tardos: Construction of locally plane graphs with many edges 29) G. Tóth: A better bound for the pair crossing number 30) U. Wagner: Minors embeddability and extremal problems for hypergraphs.