Abstract: Conformal geometry is the study of invariants which are preserved under ”angle preserving” or ”conformal” maps. In this talk, we will describe some PDE approach to the study of a class of integral conformal invariants. Start with the integral of Gauss curvature on compact surfaces, we will continue on the study of a class of integral conformal invariants on 4-manifolds with applications to the study of topology and diffeomorphism type of the class. I will describe the relevance of a 4-th order linear operator with leading symbol the bi-Laplace operator (part of the family of GJMS operator) in the study of prescribing the Gauss-Bonnet integrand on 4-manifolds under conformal change of metrics. The talk will be expository in nature with self-contained background materials.