Abstract algebra is a branch of mathematics that studies algebraic structures such as groups, rings, and fields. These structures provide a way to understand mathematical concepts through operations and relationships, allowing mathematicians to explore symmetry, solutions to equations, and more. In abstract algebra, a group is a set equipped with a single operation that satisfies certain properties, while a ring involves two operations. A field is a more advanced structure where division is also possible. This area of mathematics has applications in various fields, including cryptography, coding theory, and physics.