Hyperstructures represent a natural extension of classical algebraic structures and they were introduced in 1934 by the French mathematician Marty. Since then, hundreds of papers published on this subject. This book is devoted to the study of Semihypergroup Theory. It begins with some basic results concerning semigroup theory and algebraic hyperstructures, which represent the most general algebraic context, in which reality can be modelled. Moreover, this monograph is the first book on this theory with the title "Semihypergroup Theory." Presents an introduction to recent progress in the theory of semihypergroups. The book covers most of the mathematical ideas and techniques required in the study of semihypergroups.Employs the notion of fundamental relations to connect semihypergroups to semigroups.