I'm looking for good surveys about characteristic classes of flat real vector bundles. Letting $G$ be $\text{SL}\_n(\mathbb{R})$ with the **discrete** topology, orientable flat $n$-dimensional real vector bundles are classified by $BG$, so the characteristic classes I'm looking for are elements of the cohomology of $BG$ with respect to various systems of coefficients.


The one source I know of is Morita's book "The geometry of characteristic classes", but this is not very comprehensive or up-to-date. I also have found many references about Chern-Simons invariants, but they all seem to be written from the perspective of algebraic geometry or mathematical physics or differential geometry. I'd really like a source that is as topological as possible; for instance, for ordinary characteristic classes I prefer the approach taken in Milnor-Stashef to the approach via Chern-Weil theory. But any sources at all are welcome.



References/surveys concerning characteristic classes of flat vector bundles
I am not aware of much recent activity (after 2001, when Morita wrote his book) in this field, so I think it is still very valuable. Chern-Simons theory means something rather different today. The useful information on characteristic classes of flat vector bundles (CCFVB) seems to be scattered throughout the literature; one of the reasons might be that there is no complete picture known. Googling gives you a lot of sources, but I completely agree that a modern detailed and comprehensive exposition is missed.


Also, as far as I know, Chern-Weil theory is an indispensible ingredient of the theory. Purely topological methods are not very sensitive to flat bundles while Chern-Weil theory allows you to import methods from Lie algebra cohomology etc.


Here is a list of texts from which I learnt something on the subject:


Karoubi: Homologie cyclique et K-Theorie algebrique.


Jones, Westbury: Homology spheres, eta-invariants and algebraic K-theory. The first few sections form an informative survey which is worth reading even if you are willing to ignore the main problem they consider.


Dupont: Curvature and characteristic classes (the last section)


Kamber, Tondeur: Foliated bundles and characteristic classes 


A modern approach to CCFVB is to use differential cohomology (or differential characters). If you google, you find more information on that. 


