Additive Number Theory is a branch of mathematics that focuses on the properties and relationships of integers, particularly concerning their sums. It explores questions about how numbers can be expressed as the sum of other numbers, such as in the famous Goldbach Conjecture, which posits that every even integer greater than two can be expressed as the sum of two prime numbers. This field also investigates additive structures within sets of numbers, including arithmetic progressions and sumsets. Researchers study various problems, such as the distribution of prime numbers and the behavior of sequences, to understand the underlying patterns and principles governing these additive relationships.