Self-contained text on characteristic classes

Question

I am looking for a clear, self-contained text (either a book or lecture notes) that deals with characteristic classes, starting from the very basics (fiber bundle, principal bundle etc.), and preferably dealing with the special examples of Steifel-Whitney class and Euler class.

Thanks!

Answer 1

Milnor's book on characteristic classes is almost surely exactly what you want.

Answer 2

Bott and Tu is quite self-contained.