In Mathematics: an algebraic structure. Most of what we know about fields is from the work of Galois; hence we call it Galois Theory. For every prime p and natural n there exists a field with pn elements, which we call the Galois Field of p and n, or GF(pn). Moreover, this is how you get all finite fields. Every finite field is isomorphic to GF(pn) for some prime p and natural n.