It is generally considered that Hercules (Heracles, Herakles) was the one to rescue Theseus...
This is what is described by Apollodorus, of which some of the text can be found using the Related link:
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Theseus
Hercules.
For the dead, he established the law of judging the ghosts of the dead. For Heracles, in retrieving Cerberus from the Underworld and allowed him to take Theseus and Alcestis back to the earth with him. The deities of the Underworld, such as the Furies and the Dream gods, he was master of.
Theseis is the story of Theseus
It was a chair that Hades, one of the brothers of Zeus, had people who came to the underworld sit down on the chair so they would forget everything. Hercules once saved 1 person get off of that chair, and not the other because Theseus wanted to marry Persephone, which became the wife of Hades, God of the underworld.