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The movie is bookended by Casanova writing down an untold chapter of his life's story, though he says this particular episode is not his story to tell (and we learn why at the end). After the opening, we flash back to Giacomo Casanova as a young boy, whose mother, an actress, leaves him to be raised by his grandmother, though she promises to return one day. The scene then flashes forward to 1753 Venice, when Casanova (Heath Ledger) is a young man, and a famous fornicator. Venice is well-known for being somewhat debauched, much to the consternation of the local branch of the Inquisition. And of course, the one person the Inquisitors most want to get their hands on is Casanova, though he is protected because he is a friend of the Doge of Venice.
However, the Doge can't protect him for much longer, and warns Casanova that he will have to exile him from the city, unless he marries a suitable- read: virtuous- woman. And he can't leave Venice, because he's still waiting for his mother to return, after all these years. Of course, it's hard to find a virginal woman in Venice, but there's at least one: Victoria Donato (Natalie Dormer), who is engaged... to someone, I dunno. It's not important. But Casanova and his servant and closest friend Lupo make a case to Victoria's father, and he ends up getting engaged to her. But then he's challenged to a duel, by Giovanni Bruni, whose family lives across the canal from Victoria, and has loved her for years even though he's apparently never spoken to her, just watched her from his window. However, Giovanni is not a great swordsman, so his place is taken in the duel by his sister, Francesca (Sienna Miller). Casanova had first seen her earlier, when she had infiltrated a lecture at a local university where women were not allowed. She's a feminist, more than a century before her time, so... things aren't that easy for her, of course. But Casanova is impressed. She, of course, despises him, because by his reputation, he stands for everything she is against.
But, when they meet, she doesn't know who he is. He uses an assumed name (Salvatore, Lupo's last name, I gather) as he gets closer to her and her family (including Giovanni). However, he's not the only one keeping a secret. At first, he thinks she has a secret lover, but the man she goes to meet, Bernardo Guardi, is actually just this guy whose name she uses to publish her feminist writings, which are quite popular in Venice. Further complicating matters is the fact that Francesca's family is in debt, and her father has arranged a marriage for her to a wealthy lard merchant from Genoa, named Paprizzio (Oliver Platt). Of course, she doesn't want to marry a man she's never even met, but her mother, Andrea (Lena Olin), insists she go along with her father's plans (though this will later change, in an entertaining way). Anyway, when Paprizzio arrives in Venice, he is instead taken away by "Salvatore," who pretends to help him prepare to meet Francesca. But while Paprizzio is hidden away at Casanova's place, Casanova informs Francesca that Salvatore was an assumed name, and his real name is... Paprizzio, her fiance. Which she's not happy about at first, but she starts liking him eventually.
Meanwhile, the local Inquisition staff have been under scrutiny from Rome, which isn't happy with their failure to capture Casanova. And so, the Vatican's most feared Inquisitor, Bishop Pucci (Jeremy Irons), is sent to Venice, where he and his group send the city's Inquisitors off to preach to some equatorial natives somewhere. Cannibals, apparently. So, Pucci will constantly be trying to arrest Casanova himself, which is complicated by the fact that he has no idea what Casanova looks like, and actually Casanova gets close to the Bishop as a potential ally (despite being known as a "friend" of Casanova's). Casanova, however, is not Pucci's only target- he also wants to arrest the writer Guardi as a heretic.
Um... I hope I'm not forgetting too many of the movie's twists or anything. But there are also things I don't want to give away at all. I'll just say I found the film witty and entertaining, I enjoyed all the characters and the scenery and costumes and everything. And... that's all there is to say, I guess.