ABSTRACT
This chapter analyses the notion of groupoid from a set theoretical viewpoint, building upon the notions already developed for groups. It discusses subgroupoid as well as the basic notions which are genuine of groupoids, like the fundamental isotropy subgroupoid, connectedness and the disjoint union and direct product operations of groupoids. The chapter describes a groupoid as a disjoint union of connected groupoids and emphasizes the relationship between subgroupoids and equivalence relations. It introduces the family of cyclic groupoids, a natural generalization of cyclic groups. The chapter discusses a family of examples related to Loyd’s puzzles as well as Rubik’s pocket puzzle and its corresponding groupoid.
