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Economic applications of the theory of optimal transport have flourished in the past decade. Building on fairly recent advances in the mathematical literature, concerning the characterization of the solutions of optimal transport problems, researchers have been able to tackle a host of open questions, ranging from the theoretical analysis of matching patterns in marriage or labor markets to the resolution of difficult identification problems in econometrics. Despite its usefulness and growing importance, relatively few economists are familiar with the “modern” mathematical theory of the optimal transport problem, which is also known as the optimal assignment problem, the Monge-Kantorovich problem, or the problem of matching with transferable utility. The two main textbooks on the subject, Topics in Optimal Transportation (Villani 2003) and Optimal Transport: Old and New (Villani 2009) are excellent, but they are written …