This book introduces a new representation of probability measures, the lift zonoid representation, and demonstrates its usefulness in statistical applica- tions. The material divides into nine chapters. Chapter 1 exhibits the main idea of the lift zonoid representation and surveys the principal results of later chap- ters without proofs. Chapter 2 provides a thorough investigation into the theory of the lift zonoid. All principal properties of the lift zonoid are col- lected here for later reference. The remaining chapters present applications of the lift zonoid approach to various fields of...