  We give here a list of exact classical solutions of a large class of weakly
nonlocal theories of gravity, which are unitary and super-renormalizable (or
finite) at quantum level. It is explicitly shown that flat and Ricci-flat
spacetimes as well as maximally symmetric manifolds are exact solutions of the
equation of motion. Therefore, well-known physical spacetimes like
Schwarzschild, Kerr, (Anti-) de Sitter serve as solutions for standard matter
content. In dimension higher than four we can also have Anti-de Sitter
solutions in the presence of positive cosmological constant. We pedagogically
show how to obtain these exact solutions. Furthermore, for another version of
the theory, written in the Weyl basis, Friedmann-Robertson-Walker (FRW)
spacetimes are also exact solutions, when the matter content is given by
conformal matter (radiation). We also comment on the presence of singularities
and possible resolution of them in finite and conformally invariant theories.
"Delocalization" is proposed as a way to solve the black hole singularity
problem. In order to solve the problem of cosmological singularities it seems
crucial to have a conformally invariant or asymptotically free quantum
gravitational theory.
