Class Field Theory is a branch of algebraic number theory that studies the relationships between number fields and their abelian extensions. It provides a framework for understanding how different number fields are connected through their Galois groups, which describe symmetries in the roots of polynomials. The theory primarily focuses on the construction of field extensions that are abelian, meaning their Galois groups are abelian groups. This allows mathematicians to explore the properties of algebraic integers and ideal class groups, leading to deeper insights into the structure of number fields and their arithmetic properties.