What are the three levels of the underworld?

--Acheron: the river of woe/sorrow, the ferryman Charon ferried the dead into the Underworld via this river. Possibly a branch of the river Styx.

--Styx: the river of hate, it was said to wind around Hades nine times. Sometimes it is mentioned that Charon was responsible for ferrying the dead across this river, and this may be because the two rivers merge

--Cocytus: the river of lamentation. Cocytus flowed into the river Acheron.

--Pyriphlegethon/Phlegethon: the river of fire, it flowed into Tartarus.

--Lethe: the river of forgetfulness; those that drank from the river forgot about their former lives.

**All of the rivers but Lethe are mentioned in Homer's Odyssey. All of these rivers meet at a marsh, called by some sources the Stygian Marsh.

I should also mention Oceanus. Oceanus was a great body of water (ocean/river/stream) that encircled all of the earth. The dead entered Hades from Oceanus.

*The Regions/Sections of the Greek Underworld (in no particular order)*

Fields of Asphodel/Asphodel Meadows- This is where the shades of those people that were equally good and evil stayed.

Erebus- a region of Hades that the dead passed through shortly after dying. Mentioned more frequently in later myths.

Elysium/Elysian Fields- This is where the heroic or virtuous were sent, chosen by the gods.

Tartarus- The deepest, lowest region of Hades, it was said to be as far beneath Hades as the earth was from the heavens. In later myths it was depicted as a place of punishment, much like the Hell of Christianity.