
Abstract 
1 
Introduction and Survey 

1.1 
Survey of the scenario 

1.2 
Evidence
for asymptotic safety 

1.3 
Some working definitions 

1.4 
Relation to
other approaches 

1.5 
Discussion of possible objections 
2 
Renormalizing
the NonRenormalizable 

2.1 
Perturbation theory and continuum
limit 

2.2 
Functional flow equations and UV renormalization 

2.3 
Towards
Quantum Gravidynamics 

2.4 
Dimensional reduction of residual interactions
in UV 
3 
Asymptotic Safety from Dimensional Reduction 

3.1 
2 + 2 truncation
of Einstein gravity + matter 

3.2 
Collinear gravitons, Dirac quantization,
and conformal factor 

3.3 
Tamed nonrenormalizability 

3.4 
NonGaussian
fixed point and asymptotic safety 
4 
Asymptotic Safety from
the Effective Average Action 

4.1 
The effective average action
for gravity and its FRGE 

4.2 
Geometries at different resolution
scales 

4.3 
Truncated flow equations 

4.4 
Einstein–Hilbert and
truncations 
5 
Conclusions 
6 
Acknowledgements 
A 
Reminder on Kadanoff–Wilson
Renormalization 
B 
The Background Effective Action 

B.1 
Standard effective
action and its perturbative construction 

B.2 
Survey of background field
formalisms 

B.3 
Renormalization of Riemannian sigmamodels 
C 
The
Effective Average Action 

C.1 
Definition and basic properties 

C.2 
Flow
equation 

C.3 
Decoupling properties 

References 

Footnotes 

Figures 