Optimal transport is a vast subject and has deep connections with analysis, probability, and geometry. In recent years optimal transport has found widespread applications in data science (a notable example is the Wasserstein GAN). In this course we offer a balanced treatment featuring both the theory and applications of the subject. After laying down the theoretical foundation including the Kantorovich duality, we turn to numerical methods and their applications to data science. Possible topics include entropic regularization, dynamic formulations, gradient flows, statistical divergences and the W-GAN. Our main reference is the recent book Computational Optimal Transport by Gabriel Peyré and Marco Cuturi.