Algebraic number theory is a branch of mathematics that studies the properties of numbers through the lens of algebra. It focuses on algebraic integers, which are roots of polynomial equations with integer coefficients. This field explores how these numbers behave, their relationships, and their structures, often using concepts from both algebra and number theory. One of the key areas in algebraic number theory is the study of number fields, which are extensions of the rational numbers. Researchers also investigate ideal theory, which helps in understanding the divisibility of algebraic integers. This discipline has applications in cryptography and coding theory, making it relevant in modern technology.