Bournonville, the son of a French dancer, dominated the ballet scene in Denmark for four decades beginning in the 1830s. He created over 50 ballets for the Danish Royal Ballet, driven by fanciful plots, many based in Danish folklore. “My entire poetic sphere is Nordic,” he wrote in his memoirs. About 10 are still performed today, in part or in full. In Denmark, they are considered national treasures.

The most famous of his ballets, and the only one widely performed abroad, is “La Sylphide,” the story of James, a young Scottish farmer who is lured into the forest by a sylph on his wedding day. It’s a typical Romantic story about a dreamer who desires something beyond the mundane world in which he lives. Unlike in Bournonville’s other ballets, things end badly, for him and for the sylph. ( It is actually an adaptation of a ballet he saw in Paris .) At the Joyce, the ensemble will perform the second act — Ida Praetorius, the company’s youngest principal, will dance the role of the sylph, and Mr. Birkkjaer will be James.

But, more typically, the characters in Bournonville’s ballets live happily ever after. In “Napoli,” for example, a Neapolitan fisherman and his sweetheart, Teresina, are reunited after a miracle allows her to return safely after she is lost in a storm at sea. (Bournonville’s stories have a strong Christian influence.)

What sets the ballets apart from more familiar 19th-century works like “Swan Lake” and “The Sleeping Beauty” is that the heroes are everyday people: fishermen, farmers, soldiers, merchants. Even the magical beings, like the trolls in “A Folk Tale,” behave like people, reflecting the less honorable aspects of human nature. All the ballets include pantomime, scenes told only through gesture and facial expressions, which move the story along and add local color.