Currently, the description is
Algebraic topology is a mathematical concept that uses algebraic tools to study topological spaces. In other words, it is the intrinsic qualitative aspects of invariant spatial objects under homeomorphic transformations.
I don't think I like this, it sounds too soft.
I would suggest rewriting it as
Algebraic topology is a mathematical subject that uses algebraic objects associated to topological spaces that are invariant under homeomorphism or homotopy equivalence. We often require that these associations are functorial so that continuous maps induce morphisms of some algebraic object.
I know this is somewhat crude, and maybe overly technical, but I would be happy to see what the community might suggest for a rewrite (or even if others think the current desciption is okay.)