I'm looking for a book on advanced real Hodge Theory. I finished working through Frank Warner's Foundations of Differentiable Manifolds and Lie Groups, which ends with the Hodge Decomposition,the Hodge theorem(stating that the space of harmonic p-forms is isomorphic to the p-th Cohomology Group)as well as formulating(and proofing) the Poincare Duality. Is there any book that covers this topic further?
Thank you very much in advance.
There are too many sources of different flavors to list. If you want to start learning some differential geometry, Goldberg's Curvature and Homology is a cheap Dover book with all sorts of results with the interplay of Hodge theory and Riemannian and complex geometry.