Some mathematical disciplines can be presented and developed in the context of other disciplines, for instance Boolean algebras, that Stone has converted in a branch of ring theory, projective geome tries, characterized by Birkhoff as lattices of a special type, projec tive, descriptive and spherical geometries, represented by Prenowitz, as multigroups, linear geometries and convex sets presented by Jan tosciak and Prenowitz as join spaces. As Prenowitz and Jantosciak did for geometries, in this book we present and study several ma thematical disciplines that use the Hyperstructure Theory....