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Abstract Algebra is a branch of mathematics that studies algebraic structures such as groups, rings, fields, modules, vector spaces, and algebras. It deals with operations on these structures, their symmetries, and the relationships between them. In the context of Algebraic Geometry, abstract algebra provides the tools necessary to study geometric objects using algebraic techniques. This includes studying the symmetries of geometric objects, understanding how different geometric objects are related, and classifying geometric objects based on their algebraic properties. Thus, Abstract Algebra is a fundamental part of Algebraic Geometry, providing the algebraic machinery needed to understand and work with geometric objects in a rigorous and precise way.