  We look at the various aspects of treating general relativity as a quantum
theory. It is briefly studied how to consistently quantize general relativity
as an effective field theory. A key achievement here is the long-range
low-energy leading quantum corrections to both the Schwarzschild and Kerr
metrics. The leading quantum corrections to the pure gravitational potential
between two sources are also calculated, both in the mixed theory of scalar QED
and quantum gravity and in the pure gravitational theory. The
(Kawai-Lewellen-Tye) string theory gauge/gravity relations is next dealt with.
We investigate if the KLT-operator mapping extends to the case of higher
derivative effective operators. The KLT-relations are generalized, taking the
effective field theory viewpoint, and remarkable tree-level amplitude relations
between the field theory operators are derived. Quantum gravity is finally
looked at from the the perspective of taking the limit of infinitely many
spatial dimensions. It is verified that only a certain class of planar graphs
will in fact contribute to the $n$-point functions at $D=\infty$. This limit is
somewhat an analogy to the large-N limit of gauge theories although the
interpretation of such a graph limit in a gravitational framework is quite
different.
