I am looking for the most complete source on Cheeger-Chern-Simons invariants, Deligne cohomology and other "cohomological" topics, associated with the theory of flat bundles. I would also like to know of a place with a proof of Riemann-Hilbert correspondence in smooth case.
I have looked at the original paper by Cheeger-Simons and at the Handbook of K-theory, but it seems very strange to me that there isn't a definitive source on such an important and (as it appears to me) well-understood topic.
As for Riemann-Hilbert correspondence, are Bolibrukh's papers the right place to look for the modern proof?