The Troll's Daughter is a Danish fairy tale. Andrew Lang included it in The Pink Fairy Book.
Ruth Manning-Sanders included it, as "The Troll's Little Daughter", in A Book of Ogres and Trolls.
A youth got a place with a stranger, who offered him six bushels of money to serve him three years, obeying him in everything. He took him to a home on a bank in a great forest, because the stranger was a troll. The first day, the troll had him feed all the wild animals in the forest, which it had tied up. The next, the troll turned him into a hare and set him wild to run the year long. Every hunter tried to get him, as the only animal in the forest, but no dog could catch him and no gun shoot him.
The troll summoned him back, like any other animal, turned him back into a man, and asked how he liked it. The youth answered that he had never been able to run like that before; he liked it. He fed the wild animals again, and for the next year was a raven. When the troll turned him back, he told him he liked rising so high. He fed the wild animals again and for the next year was a fish. Deep in the sea, he found a palace where a beautiful maiden lived. He tried to remember the words the troll had said, and turned himself into a man in that palace. He spent time with her; she quickly got over her fright and was glad not to be alone. But she told him the time was near and he had to become a fish again. She also told him she was the troll's daughter, and he imprisoned her here. All the kings about were in debt to the troll. If they were to see each other again, he must enter the service of a king who owed the troll six bushels of coins. Then he should offer to pay the king's debts in return for coming; once he came, he would make trouble for the troll until it demanded the king answer three questions for his life. They would be where his daughter was, and then to pick her out, and then to find the troll's heart, which was in a fish.
He went back to the troll and refused to stay in his service. He served the king and did as the troll's daughter had said. When he got to the troll's castle with the king, he broke all sorts of glass things. Then he answered the troll's questions. When he picked out his daughter, the maiden appeared and stayed by him; when he picked out the fish the maiden indicated, he cut it open and killed the troll. This destroyed all the bonds the troll had from the kings in debt to him, and freed all the wild animals.
The youth married the maiden. All the kings he had freed from the troll took him as their emperor.