This chapter addresses the so-called inverse problem of Lie groups analysis of differential equations. It consists in the determination of a differential equation admitting a given Lie algebra of point symmetries. To fix the language, the basic notions of differential geometry, with a focus on the geometry of differential equations, are briefly reviewed. In such a way, the analytical properties of Lie groups are presented within the more natural differential geometric framework. Then, the notions of strongly Lie remarkable equations and weakly Lie remarkable equations are introduced, and necessary and sufficient conditions are established. Various examples of differential equations—both partial and ordinary—uniquely determined by Lie algebras of symmetries are characterized. In particular, the family of Monge–Ampère equations and the equations of minimal surfaces are analyzed. Some important Lie algebras (isometric, affine, projective, and conformal) are considered, and the corresponding Lie remarkable equations, either weak or strong, are characterized.