This book collects the scientific contributions of a group of leading experts who took part in the INdAM Meeting held in Cortona in September 2014. With combinatorial techniques as the central theme, it focuses on recent developments in configuration spaces from various perspectives. It also discusses their applications in areas ranging from representation theory, toric geometry and geometric group theory to applied algebraic topology.

1 Alexander I. Suciu: Around the tangent Cone Theorem.- 2 Graham Denham: Higher Resonance Varieties of Matroids.- 3 Nicole Berline and Michèle Vergne: Local asymptotic Euler-Maclaurin Expansion for Riemann Sums over a semi-rational Polyhedron.- 4 Andrzej Weber: Leray spectral Sequence for Complements of certain Arrangements of smooth Submanifolds.- 5 Sergey Yuzvinsky: Higher topological Complexity of Artin Type Groups.- 6 Armindo Costa and Michael Farber: Random simplicial Complexes.- 7 Dmitry N. Kozlov: Combinatorial Topology of the standard chromatic Subdivision and Weak Symmetry Breaking for 6 Processes.- 8 Emanuele Delucchi and Tim Lindemann: Cryptomorphisms for abstract Rigidity Matroids.- 9 Jeremiah Bartz: Induced and complete Multinets.- 10 Alexandru Dimca and Gus Lehrer: Cohomology of the Milnor Fibre of a Hyperplane Arrangement with Symmetry.- 11 Mario Salvetti and Matteo Serventi: On the twisted Cohomology of a_ne Line Arrangements.- 12 Elizabeth Leyton Chisholm and Jon McCammond: Braid Groups and euclidean Simplices.- 13 Rita Jiménez Rolland: The Cohomology of M0,n as an FI-module.- 14 Matthias Franz: Syzygies in equivariant Cohomology for non-abelian Lie Groups.- 15 Frederick R. Cohen and Mentor Stafa: A Survey on Spaces of Homomorphisms to Lie Groups.