The astronomical study of the planet Pluto.
The study of the planets is generally named after Greek gods, while the planets themselves are generally named after Roman gods. Pluto, the Roman god of the underworld, corresponds to the Greek god Hades.
The word hadeology isn't in common usage today, and is likely to be found only in collections of curious words or in works of science fiction.
If you came here by accident, you might be looking for the word demonology.