TITLE: Books in advanced differential topology
QUESTION [16 upvotes]: I am looking for books or other sources in differential topology that include topics like: vector bundles, fibration, cobordism, and other related topics.
In general, if anyone has recommendation of books of advanced differential topology I would like to hear (I've already read Bott&TU, Warner).
Thanks!

REPLY [2 votes]: Let me mention a recent book:
Differential Cohomology: Categories, Characteristic Classes, and Connections, edited by Araminta Amabel, Arun Debray and Peter J. Haine, available on arXiv.
It is assembled from talks in a graduate student seminar. Although most of content is classical, the treatment is relatively modern, using $\infty$-categories, $\infty$-topoi and methods in motivic cohomology à la Voevodsky.