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Here is what the book says:

Definition 2.1 (Binary Operations, Groupoids, and Groupoid

Automorphisms). A binary operation + in a set S is a function + :

S x S -> S. We use the notation a + b to denote +(a, b) for any a, b in S.

A groupoid (S, +) is a nonempty set, S, with a binary operation, +. An

automorphism phi of a groupoid (S, +) is a bijective (that is, one-to-one)

self-map of S, phi : S -> S, which preserves its groupoid operation, that is,

phi(a + b) = phi(a) + phi(b) for all a, b in S.

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.