An Invitation to Optimal Transport, Wasserstein Distances, and Gradient Flows

This book provides a self-contained introduction to optimal transport, and it is intended
as a starting point for any researcher who wants to enter into this beautiful subject.

The presentation focuses on the essential topics of the theory: Kantorovich duality, existence and uniqueness
of optimal transport maps, Wasserstein distances, the JKO scheme, Otto’s calculus, and Wasserstein gradient
flows. At the end, a presentation of some selected applications of optimal transport is given.

Suitable for a course at the graduate level, the book also includes an appendix with a series of exercises
along with their solutions. The present second edition contains a number of additions, such as a new section
on the Brunn–Minkowski inequality, new exercises, and various corrections throughout the text.