Adeles are mathematical objects used in number theory, particularly in the study of algebraic numbers and algebraic groups. They provide a way to combine information from various completions of a number field, such as the rational numbers, real numbers, and p-adic numbers. This unification helps mathematicians analyze properties of numbers and their relationships more effectively. In the context of number theory, adeles are often used in conjunction with adelic topology and automorphic forms. They play a crucial role in modern research, including areas like Langlands program, which seeks to connect number theory with representation theory. Adeles help in understanding the structure of solutions to equations and the behavior of numbers across different fields.