Some myths say he cannot, that he must remain there. But others state that he can, for example when he claimed Persephone, he left the underworld to claim her.
He is also permitted to enter Mt. Olympus, but he chooses not to because the other Gods find him depressing and morbid.
So, in my personal opinion I would say yes, he probably can leave the Underworld as he pleases, but does not have much of a reason to most of the time. Since the Underworld is his Kingdom.
He can come and go to and from the Underworld anytime he pleases; for council on Olympus, for battles, and such of that like.
To take Persephone, daughter of Demeter and Zeus, to the Underworld as wife.
Hades' Underworld is called The Underworld.
There was no ruler of the Underworld before Hades.
Hades was keeping her a prisoner in the Underworld and she ate some of the food of the underworld, which means you are never allowed to leave.
He can come and go to and from the Underworld anytime he pleases; for council on Olympus, for battles, and such of that like.
yes
Hades had his own realm of which he was King, that of the Underworld, and Hades did not often leave it.
To take Persephone, daughter of Demeter and Zeus, to the Underworld as wife.
Hades' Underworld is called The Underworld.
Hades is the God of the Underworld.
Hades resides in the Underworld.
No, He just makes sure they do not leave the underworld.
Demeter never actually goes to the Underworld. When it is time for Persephone to leave Hades, Demeter sends Hermes to the Underworld instead.
Persephone rules the Underworld with Hades; she ate of the pomegranate so can not leave the Underworld entirely every year.
Yes, Hades was/is the ruler of the Underworld.
The Underworld was given to Hades as his reign.