There is no question what topology is and what it's about: it's about topologies (= topological spaces), and that's it.
There is also no question what (universal) algebra is and what it's about. (Among other things, it's about algebras.)
But what is geometry and what is it about? Is there a thorough and generally agreed upon definition of a geometry (= geometric structure) comparable to the unequivocal definition of a topology?