A finite field is a set of numbers that contains a finite number of elements, where you can perform addition, subtraction, multiplication, and division (except by zero) while still staying within the set. These fields are essential in various areas of mathematics, particularly in algebra and number theory. Finite fields are often denoted as GF(p^n), where p is a prime number and n is a positive integer. The simplest example is GF(2), which consists of the elements 0, 1. Finite fields are widely used in cryptography, coding theory, and combinatorial design.