Offenbach's opera is in five acts, with first and last acts serving as a prologue and epilogue.
In ACT ONE, Hoffmann is drinking in Luther's tavern, near the opera house in Nuremberg. As always, he's accompanied by his muse, who wants to cure the poet of his unhappy love for Stella, a beautiful singer. The muse then takes the identity of the poet's student friend Nicklausse. We also meet a counselor called Lindorf — Hoffmann's rival for Stella's love.
The crowd at the tavern knows Hoffmann's skill at storytelling, and he entertains them with the tale of Kleinzach, a legendary dwarf. But Hoffmann is preoccupied by romance, and his mind keeps wandering into thoughts of beautiful women he has loved. The crowd decides to humor him, and wants to hear all of his love stories. Hoffmann agrees, and everyone settles down to listen.
The first story is told in ACT TWO. Hoffmann has fallen for Olympia, the daughter of an inventor named Spalanzani. But this "daughter" is actually one of Spalanzani's inventions: a mechanical doll. Spalanzani is expecting a house full of guests, and plans to introduce his new invention to the public. But he's worried about one guest in particular, a gadget-maker named Coppelius who provided Olympia's eyes. Spalanzani is afraid Coppelius will want a percentage of the action. He decides to buy him out, and writes Coppelius a check.
When all the guests have assembled, Spalanzani trots out Olympia, winds her up, and puts her through her paces. The doll can even sing, and comes up with a coloratura aria — but she slows down every now and then, and has to be rewound. Hoffmann is so in love with her that he doesn't notice.
But the jig is up when Coppelius returns. Spalanzani's check has bounced, and Coppelius gets even by destroying Olympia. At first, Hoffmann is horrified, watching as the woman he loves is torn limb from limb. Then he realizes what's really happening, and the guests all mock him as the act ends.
In ACT THREE, Hoffmann is love with Antonia, a beautiful young woman suffering from a serious illness. She lives with her father, Crespel, and their house is filled with musical instruments, which Crespel makes himself. There's a place of honor reserved for a picture of Crespel's dead wife, Antonia's mother.
Antonia is at the piano and begins to sing a sad song, but Crespel rushes in to stop her. Though Antonia loves singing, the exertion is dangerous for her, and threatens her life.
Crespel leaves again, and against his wishes, Hoffmann and Nicklausse come to pay Antonia a visit. She and Hoffmann sing together, declaring their love. When Crespel returns, Antonia runs to her room. Hoffmann hides, and overhears a heated conversation between Crespel and Dr. Miracle, who has come to treat Antonia. The doctor also treated Antonia's mother, and Crespel thinks Miracle was responsible for her death.
When the two men leave, Hoffman goes to Antonia and persuades her to stop singing. But when Hoffmann has gone, Miracle returns. He calls for Antonia, and somehow conjures the voice of her mother, which seems to emanate from the dead woman's portrait. Taking up one of Crespel's violins, Miracle urges Antonia to sing along. She does, but the stress is too much for her, and she collapses. Hoffmann and Nicklausse rush back into the house just as Dr. Miracle pronounces Antonia dead.
ACT FOUR takes place in Venice, and begins with Hoffmann on the balcony of a palace, overlooking the Grand Canal. Below, Nicklausse and the glamorous courtesan Giulietta are floating in a gondola. Hoffmann listens as the two sing a gentle barcarolle, the opera's most famous melody.
Inside, there's a lively party going on, and Hoffmann encounters Giulietta. He's been falling in love with her, despite warnings from Nicklausse. Giulietta already has a lover, a man called Schlemil, but that seems to make her even more attractive to Hoffmann.
Before long, we meet this story's villain, a magician named Dapertutto. He makes Giulietta a tempting offer. Dapertutto promises her a diamond ring if she'll bring him Hoffmann's "other self" — that is, if she can steal his reflection. Giulietta agrees, and goes into action.
She takes Hoffmann into another room. He finds her irresistible, and the two sing a rapturous duet. Giuletta asks Hoffmann for his reflection, as a keepsake. He agrees, and immediately discovers that he can no longer see himself in the mirror. Schlemil then bursts in, surprising the lovers. Giuletta runs off to hide in her private room. Schlemil challenges Hoffmann to a duel and is killed.
Hoffmann finds the key to Giulietta's room on a chain around Schlemil's neck. But when he opens her door, he finds her in a passionate embrace with a servant, Pitichinaccio. Dapertutto breaks into a sinister laugh, as Nicklausse drags Hoffmann away.
ACT FIVE is a brief epilogue. We're back in Nuremberg, at Luther's tavern, and Hoffmann has finished his sad stories. He orders more wine, to dampen his memories. Then Stella appears, fresh from a triumphant night at the opera, and approaches Hoffmann. But when he looks at her, he's reminded of the three lovers he lost in his stories, and he turns her away. Unperturbed, Stella leaves with Hoffmann's rival, Lindorf.
Nicklausse stays with Hoffmann, and again becomes the poet's muse-- urging Hoffmann to go back to his writing, and saying that sorrow will make his poetry all the wiser.
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