That’s odd, I’ve already taken courses covering the material described in that course. The functional analysis course I wanted to take covers:

Banach and Hilbert spaces, bounded linear maps, Hahn-Banach theorem, open mapping theorem, closed graph theorem, topologies, nets, Hausdorff spaces, dual spaces, weak topologies, Tychonoff’s theorem, Banach-Alaoglu theorem, reflexive spaces.

Interesting how they split things up differently.