An Overview of the Foundations of the Hypergroup Theory

This paper is written in the framework of Special Issue Mathematics entitled “Hypercompositional Algebra and Applications”, focuses on presentation essential principles hypergroup, which prominent structure hypercompositional algebra. In beginning, it reveals structural relation between two fundamental entities abstract algebra, group hypergroup. Next, presents several types hypergroups, derive from enrichment hypergroup with additional axioms besides ones was initially equipped with, along their properties. Furthermore, analyzes studies various subhypergroups that can be defined hypergroups combination ability to decompose into cosets. The exploration this far-reaching concept highlights particularity theory versus theory, demonstrates different techniques special tools must developed order achieve results