What is a groupoid? I'm reading a book about gyrovectors and in the first chapter it starts defining something which it calls it a groupoid but doesn't inform the reader about its axioms. so I felt uncomfortable to face a new mathematical definition without knowing the axioms that it should satisfy. Here is what the book says: What axioms should a groupoid satisfy? and what's the difference between a groupoid and group? because the name apparently has been derived from the word group.