I've just taken an introductory course on Riemannian Geometry. I've read several chapters of Do Carmo's book Riemannian Geometry and O'Neill's one on Semi-Riemannian Geometry. Also, I am familiarized with the theory of Differentiable Manifolds (I've read the classical books of Warner, Postnikov, Kumaresan, Boothby...), Lie groups and algebras and Algebraic Topology. I am wondering if does anyone know any lectures or books developing the theory of Riemannian (or Semi-Riemannian) geometry in terms of differential forms. I know the classical lectures by Élie Cartan on the moving frame's method (repere mobile) and the Differential Geometry books of M. Spivak are quite good references.
Thanks in advance!