Books and Surveys:

• Galichon. Optimal Transport Methods in Economics. Princeton, 2016.

• McCann. A glimpse into the differential topology and geometry of optimal transport. Discrete Contin. Dyn. Syst., 34:1605–1621, 2014.

• McCann and Guillen ‘Five lectures on optimal transport’ In Analysis and Geometry of Metric Measure Spaces. G. Dafni et al, eds. Providence: Amer. Math. Soc. (2013) 145-180.

• Peyré and Cuturi, Computational Optimal Transport, 2017.

• Santambrogio. Optimal Transport for Applied Mathematicians. Springer, 2015.

• Villani. Topics in Optimal Transportation. AMS, 2003.

• Villani. Optimal Transport: Old and New. Springer, 2009.

For more references, see http://www.math.toronto.edu/mccann/assignments/1502/books.pdf.