Riemannian and conformal geometry are classical topics of diﬀerential geometry.
Even though both kinds of geometries are much related and have many common questions
and features, they are very diﬀerent in nature. In fact, conformal geometry is a special kind
of parabolic geometry, i.e., a geometry of 2nd order. In my talk I will explain basic notions
of conformal geometry from the viewpoint of parabolic geometry. Then I will feature some
interesting topics and compare these with Riemannian geometry. In particular, I will discuss
conformal holonomy and geodesics, and I will introduce a notion of conformal Einstein manifolds.