**About**

A vast amount of observational data has made Einstein's General Relativity (GR) the best current theory to describe classical aspects of the gravitational interaction. However, despite its great success there are still fundamental questions that remain unanswered. On short-distance scales GR predicts the existence of black-hole and cosmological big-bang singularities where spacetime terminates and the theory breaks down. Moreover, Einstein's theory lacks predictability in the high-energy regime, being perturbatively non-renormalizable. It is generally believed that a self-consistent theory of quantum gravity is necessary to deal with these issues and complete Einstein's GR in the short-distance and high-energy regimes.

A natural way to extend GR in the high-energy regime is to generalize the Einstein-Hilbert Lagrangian by adding higher powers of the curvature tensors and, indeed, in 1977 K. Stelle showed that quadratic curvatures were already sufficient to formulate a renormalizable theory of quantum gravity. However, such additional terms were also shown to introduce a “

A natural way to extend GR in the high-energy regime is to generalize the Einstein-Hilbert Lagrangian by adding higher powers of the curvature tensors and, indeed, in 1977 K. Stelle showed that quadratic curvatures were already sufficient to formulate a renormalizable theory of quantum gravity. However, such additional terms were also shown to introduce a “

**ghost**” degree of freedom because of higher order time-derivatives which cause classical Hamiltonian instabilities and break unitarity at the quantum level. This moment in the history of Theoretical Physics - more than forty years ago - can be considered as the beginning of many new attempts aimed at formulating a consistent quantum theory of gravity, and thus at solving both issues of**renormalizability**and**unitarity**of the gravitational interaction.**Contents**

To achieve a thorough assessment of the role and the true meaning of higher, or even infinite, derivatives in the quantization of gravity, in this workshop different point of views will be presented and several approaches to quantum gravity will be covered, among which

Furthermore, applications of quantum gravity, higher derivatives and nonlocality will be discussed in the context of

******Asymptotically safe gravity****Effective field theory of gravity****Four-derivative gravity with unstable ghosts****Hořava–Lifshitz gravity****Metric-affine quantum gravity********Nonlocal theories of gravity****PT-symmetric quantization****Self-completion of general relativity****String field theory**

Furthermore, applications of quantum gravity, higher derivatives and nonlocality will be discussed in the context of

**cosmology**,**black-hole physics**and**spacetime singularities**.