  In this book, we study Gromov's metric geometric theory on the space of
metric measure spaces, based on the idea of concentration of measure phenomenon
due to L\'evy and Milman. Although most of the details are omitted in the
original article of Gromov, we present complete and detailed proofs for some
main parts, in which we prove several claims that are not mentioned in any
literature. We also discuss concentration with a lower bound of curvature,
originally studied by Funano and the author.
