I love that it provides a systematic way of thinking about structures and proving properties of said structures that I am working with in code. It's amazingly powerful to say "type t defines a monoid with operation k: t -> t and identity Nil" because it comes with a whole slew of properties and theorems. It meshes very well with strongly typed functional languages that support algebraic data types (e.g. Haskell and OCaml).

I don't much care for theoretical abstract algebra (e.g. non-abelian groups of order 18) and I am by no means a master (or even an amateur!) but I find abstract algebra's concepts useful and I hope to learn more!