How does the study of abstract algebraic structures help you

Abstract algebra is the set of advanced topics of algebra that deal with abstract algebraic structures rather than the usual number systems. The most important of these structures are groups, rings, and fields. Important branches of abstract algebra are commutative algebra, representation algebra, and homological algebra.
1) Abstract algebra unifies many principles learned at earlier stages of mathematics. Matrices, polynomials, vector spaces, modular arithematic, and more all suddenly get classified into set theoretic ideas called algebraic structures. Once you learn about groups, rings, fields, modules, etc., it is impossible to un-see them. Abstract algebra filters out a lot of the specific details about all these objects and unifies them in relatively easy to remember chunks.
2) Abstract algebra gives insight into the structure of symmetries. This is specificially about group theory, but the realisation that symmetry-preserving actions compose to create another symmetry-preserving action is indicative of the fact that symmetry actions form a group. Now, this leads to a type of group called the symmetric group. Because the symmetric group exists, now every theorem in abstract algebra about abstract groups applies.
3) Abstract algebra gives us the ability to gain new understandings about other topics. The existence of fields like algebraic topology, algebraic geometry, algebraic coding theory, etc. shows that the ideas of abstract algebra give us many new clarifying insights and allow us to build some pretty cool mathematical machinery.
4) abstract algebra also has applications in physics, statistics and functional programming.