>>11443002Lots of things in math look like numbers.
We learn adding and subtracting numbers in school. oh hey you can add fractions too! you can even add function and polynomials, and matrices, and vectors...
What abstract algebra does is generalize operations and structures so we can study them instead of their numerous concrete forms.
What properties are necessary for addition and multiplication to make sense? What structures have them? Once you understand them you can apply them to many mathematical situations.
Besides unlocking connections between mathematical structures, it is useful to abstract because it teaches you the essential features that make something work. This often makes hard problems easier than they would be if you have too many details.
See also the study of vector spaces, metric spaces, etc
