Title: "Local Conformal Symmetry and its Violation at Quantum Level"
The purpose of this talk is to present a short review of the local
conformal symmetry in curved $4d$ space-time. Furthermore we
discuss the conformal anomaly, anomaly-induced effective actions
and existing ambiguities. Despite the conformal symmetry is
always broken at quantum level, it may be a basis of useful and
interesting approximations for investigating quantum corrections.
These quantum corrections represent an appropriate basis for a
number of applications in cosmology and black hole physics.