Mathematical structures are frameworks that help organize and understand mathematical concepts. They consist of sets, operations, and relations that define how elements interact with one another. Common examples include groups, rings, and fields, each with specific properties and rules that govern their behavior. These structures provide a way to study mathematical objects systematically. For instance, in a group, the focus is on a set equipped with a single operation that satisfies certain axioms, such as closure and associativity. This allows mathematicians to explore deeper relationships and patterns within mathematics.