  In this paper, we introduce and motivate the studies of Quantum Weyl Gravity
(also known as Conformal Gravity). We discuss some appealing features of this
theory both on classical and quantum level. The construction of the quantum
theory is described in detail to the one-loop level. To facilitate computations
we use only physical degrees of freedom, which are singled out through the York
decomposition. At the one-loop level we compute the partition function around a
general Einstein space. Next, the functional renormalization group of couplings
in Quantum Weyl Gravity is investigated. We reproduce completely previous
results obtained on maximally symmetric and Ricci-flat backgrounds. Finally, we
comment on further directions and on the issue of conformal anomaly.
