The theory of hyperidentities generalises the equational theory of universal algebras and is applicable in several fields of science, especially in computer sciences. This book presents the theory of hyperidentities and its relation to clone identities.The basic concept of a hypersubstitution is used to introduce the monoid of hypersubstitutions, hyperidentities, M-hyperidentities, solid, and M-solid varieties. Hypersubstitutions lead to conjugate pairs of additive closure operators. In the book the theory of such pairs of closure operations is developed. Along with this general theory, these concepts are also examined for specific varieties of algebras, especially for varieties of semigroups.This work integrates into a coherent framework and notation many results scattered throughout the literature over the last eighteen years. In addition, the book contains some applications of hyperidentities to the functional completeness problem in multiple-valued logic.

The general theory is also extended to partial algebras. The last chapter contains a list of exercises and open problems with suggestions for future work in this area of research.