This book is the first comprehensive introduction to the theory of mass transportation and its many applications. It presents a novel approach by combining a survey of the topic with a chapter of problems, making it an excellent graduate textbook. The theory of mass transportation began with Monge's 1781 definition of optimal transportation, followed by Kantorovich's 1942 application of linear programming to the problem, and later by Brenier's 1987 proof of a projection theorem. These contributions marked the beginning of a mathematical theory with many unexpected ramifications. Today, the Monge-Kantorovich problem is studied by researchers from diverse fields, including probability theory, functional analysis, isoperimetry, partial differential equations, and meteorology. The book is not intended to be exhaustive but rather serves as an introduction. It is complemented by other reference texts, such as the two-volume work by Rachev and Rüschendorf, and lecture notes by Ambrosio and Urbas. While the book does not go deeply into some aspects, such as the L¹ theory or regularity theory, it provides a good elementary reference for topics like displacement interpolation and the differential viewpoint of Otto. The proofs are kept simple and accessible to non-expert students. The book is intended for graduate students and researchers, requiring only basic knowledge of measure theory and functional analysis.This book is the first comprehensive introduction to the theory of mass transportation and its many applications. It presents a novel approach by combining a survey of the topic with a chapter of problems, making it an excellent graduate textbook. The theory of mass transportation began with Monge's 1781 definition of optimal transportation, followed by Kantorovich's 1942 application of linear programming to the problem, and later by Brenier's 1987 proof of a projection theorem. These contributions marked the beginning of a mathematical theory with many unexpected ramifications. Today, the Monge-Kantorovich problem is studied by researchers from diverse fields, including probability theory, functional analysis, isoperimetry, partial differential equations, and meteorology. The book is not intended to be exhaustive but rather serves as an introduction. It is complemented by other reference texts, such as the two-volume work by Rachev and Rüschendorf, and lecture notes by Ambrosio and Urbas. While the book does not go deeply into some aspects, such as the L¹ theory or regularity theory, it provides a good elementary reference for topics like displacement interpolation and the differential viewpoint of Otto. The proofs are kept simple and accessible to non-expert students. The book is intended for graduate students and researchers, requiring only basic knowledge of measure theory and functional analysis.