This reference book on the Skyrme model of hadron matter aims at presenting to researchers and advanced undergraduate students the current state of the art of this simplest description of hadron structure and interactions. Having traced the evolution of the model from Skyrme's ideas as given in his pioneering papers, the book gives a thorough overview of relevant problems that can serve as an introduction for researchers who are new to this field. Furthermore, multidimensional nonlinear models are discussed, such as the generalization of Hobart-Derrick's theorem. A set of appendices with technical derivations and a list of references complete the book.