TITLE: Wasserstein distance and the Kantorovich-Rubinstein duality
QUESTION [6 upvotes]: The only few references I could find on this topic are either amateur blog posts (http://n.ethz.ch/~gbasso/download/A%20Hitchhikers%20guide%20to%20Wasserstein/A%20Hitchhikers%20guide%20to%20Wasserstein.pdf and https://vincentherrmann.github.io/blog/wasserstein/) or the 1000 page tome by Cedric Villani, (http://cedricvillani.org/wp-content/uploads/2012/08/preprint-1.pdf)
Is there any expository reference/lecture notes about this which is somewhere between the two kinds of references above? Any paper by maybe Cedric Villani himself which covers all these grounds?

REPLY [2 votes]: Kantorovich himself wrote a very detailed exposition which constitutes Section 8.4 of  Functional Analysis by Akilov and Kantorovich