• Quantum Gravity — A Short Overview.- The Search for Quantum Gravity Effects.- Time Paradox in Quantum Gravity.- Differential Geometry in Non-Commutative Worlds.- Algebraic Approach to Quantum Gravity III: Non-Commmutative Riemannian Geometry.- Quantum Gravity as a Quantum Field Theory of Simplicial Geometry.- An Essay on the Spectral Action and its Relation to Quantum Gravity.- Towards a Background Independent Formulation of Perturbative Quantum Gravity.- Mapping-Class Groups of 3-Manifolds in Canonical Quantum Gravity.- Kinematical Uniqueness of Loop Quantum Gravity.- Topological Quantum Field Theory as Topological Quantum Gravity.- Strings, Higher Curvature Corrections, and Black Holes.- The Principle of the Fermionic Projector: An Approach for Quantum Gravity?.- Gravitational Waves and Energy Momentum Quanta.- Asymptotic Safety in Quantum Einstein Gravity: Nonperturbative Renormalizability and Fractal Spacetime Structure.- Noncommutative QFT and Renormalization.

From the reviews: "Presents a selection of contributions presented at the workshop 'Mathematical and Physical aspects of Quantum Gravity' ... . presentation of various approaches to quantum gravity in one volume is rather unique and provides reader with an opportunity to compare their advantages and disadvantages. A significant advantage of this volume is that the articles are written in a less technical style, focusing only on major theoretical questions, with many contributions being accessible to non-specialists and thus providing a broad overview of this fascinating field of research." (Vojtech Pravda, Applications of Mathematics, Vol. 55 (5), 2010)