I am curious to know some theorems usually taught in advanced math courses which are considered 'generalizations' of theorems you learn in early university or late high school (or even late university).

For example, I know that Stokes's theorem is a generalization of the divergence theorem, the fundamental theorem of calculus and Green's theorem, among I'm sure many other notions.

I've read that pure mathematics is concerned mostly with the concept of 'generalization' and I am wondering which theorems/ideas/concepts, like Stokes's theorem, are currently celebrated 'generalizations' by mathematicians.

For example, I know that Stokes's theorem is a generalization of the divergence theorem, the fundamental theorem of calculus and Green's theorem, among I'm sure many other notions.

I've read that pure mathematics is concerned mostly with the concept of 'generalization' and I am wondering which theorems/ideas/concepts, like Stokes's theorem, are currently celebrated 'generalizations' by mathematicians.