A Number Field is a mathematical concept in the area of algebraic number theory. It is defined as a finite field extension of the rational numbers, denoted as ℚ. This means that a number field contains numbers that can be expressed as solutions to polynomial equations with rational coefficients. Number fields are important for studying the properties of integers and rational numbers in a broader context. They allow mathematicians to explore concepts like algebraic integers, ideal theory, and class groups. Each number field can be represented by its degree, which indicates the dimension of the field as a vector space over ℚ.