Literature concerning characteristic classes? It sounds like the literature about characteristic classes is not very abundant (am I wrong?). 
Whenever I look for books dealing with this matter, I'm always led to the same material like the classical book Characteristic Classes (J. Milnor, J. Stasheff). Thus I'm looking for different approaches and expositions. 
Can anyone recommend to me some (modern) references concerning characteristic classes?
 A: Characteristic Classes by J. Milnor and J. Stasheff is classic and (in my opinion) must be read.
Vector bundles and K-theory notes by Hatcher is very good for the first reading.
If you don't like axiomatic definitions and want to see geometrically Thom class and Thom isomorphism(which are kind of building blocks for characteristic class theory) and their relation to Poincare duality, the best material(in my opinion) is Bott and Tu.
Husemoller discusses characteristic classes from many different point of views and it's a good book for vector bundles and fibre bundles(by good I mean he gives details for some constructions while some authors leave them as exercises). (but not modern)
If you want to understand Chern-Weil theory of characteristic classes then Morita is a good book to look at. It does not require much background and it's like Bott and Tu but differential geometric point of view not algebraic topology.
If you are looking for short(according to its content) notes (may be with some background), you can look at Cohen's note.
