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 p^{n} elements, which we call the Galois Field of p and n, or GF(p^{n}). Moreover, this is how you get all finite fields. Every finite field is isomorphic to GF(p^{n}) for some prime p and natural n.