Quantum physics has been highly successful for more than 90 years. Nevertheless, a rigorous construction of interacting quantum field theory is still missing. Moreover, it is still unclear how to combine quantum physics and general relativity in a unified physical theory. Attacking these challenging problems of contemporary physics requires highly advanced mathematical methods as well as radically new physical concepts.

Preface.- Christopher J. Fewster. On the Spin-Statistics Connection in Curved Spacetimes.- Daniel Becker, Martin Reuter. Is there a C-Function in 4D Quantum Einstein Gravity?.- José M. Gracia-Bondía.Systematic Renormalization at all Orders in the DiffRen and Improved Epstein{Glaser Schemes.- Michael Dütsch. Higgs Mechanism and Renormalization Group Flow:Are They Compatible?.- Claudio Dappiaggi. Hadamard States From Null Infinity.- Michael Gransee.Local Thermal Equilibrium States in Relativistic Quantum Field Theory.- Frédéric Paugam. Categorical Methods in Quantum Field Theory.- Harald Grosse, Raimar Wulkenhaar.A Solvable Four-Dimensional QFT.- Rainer Verch. Wave Equations with Non-Commutative Space and Time.- Gandalf Lechner, Jan Schlemmer.Thermal Equilibrium States for Quantum Fields on Non-Commutative Spacetimes.- Christian Fleischhack.Kinematical Foundations of Loop Quantum Cosmology.- Gerhard Börner.Cosmic Puzzles - Dark Matter and Dark Energy.- Israel Michael Sigal.Radiation and Scattering in Non-Relativistic Quantum Electrodynamics.- Stefan Teufel, Roderich Tumulka. Avoiding Ultraviolet Divergence by Means of Interior{Boundary Conditions.- Felix Finster.Causal Fermion Systems - An Overview.- Dirk-André Deckert, Franz Merkl. A Perspective on External Field QED.- Enno Keßler.Super Riemann Surfaces and the Super Conformal Action Functional.- Stefan Waldmann. Recent Developments in Deformation Quantization.- Michael K.-H. Kiessling.Dirac's Point Electron in the Zero-Gravity Kerr - Newman World.- Christoph A. Stephan. Noncommutative Geometry and the Physics of the LHC Era.- Klaus Kröncke. Variational Stability and Rigidity of Compact Einstein Manifolds.- Index.