Analysis on Polish spaces and an introduction to optimal transportation General topology Metric spaces Polish spaces and compactness Semi continuous functions Uniform spaces and topological groups Càdlàg functions Banach spaces Hilbert space The Hahn Banach theorem Convex functions Subdifferentials and the legendre transform Compact convex Polish spaces Some fixed point theorems Abstract measure theory Further measure theory Borel measures Measures on Euclidean space Convergence of measures Introduction to Choquet theory Optimal transportation Wasserstein metrics Some examples