Group Theory 

If you see what I mean.
A case in point is an area of mathematics called Group Theory. There are many cases where we have a collection of things, along with some way of combining them in specific way are classified as groups. Examples are numbers (which we can add or subtract) and rotations (which we can combine by doing one after the other).
Galois did a lot with group theory, to the point where there's a subtopic call Galois Theory.