New ideas - and there are many of them for this is an exciting field of research - often diverge to a degree where it seems impossible to decide in which of the many possible direction(s) the ongoing developments should be further sustained.
The division of the book in two (overlapping) parts reflects the duality between the physical vision and the mathematical construction. The former is represented by tutorial reviews on non-commutative geometry, on space-time discretization and renormalization and on gauge field path integrals. The latter one by lectures on cohomology, on stochastic geometry and on mathematical tools for the effective action in quantum gravity.
The book will benefit everyone working or entering the field of quantum gravity research.
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"This volume contains the extended proceedings of the Summer School: New Paths Towards Quantum Gravity held in Holbæk, in Denmark. ... I really recommend this book for your personal library. It is one of the best physics books I have been in contact in the last years." (Philosophy, Religion and Science Book Reviews, bookinspections.wordpress.com, January, 2014)