Princess Ida

The longest Gilbert and Sullivan operetta, poking fun at Straw Feminist tendencies, women's education in general and possibly early bethrothals as well.

The titular princess was married to the nearby kingdom's Prince Hilarion when they were one and two years old, respectively. Twenty years have passed since and the courtiers of Castle Hildenbrand impatiently await the arrival of King Gama and his daughter. Instead, the king arrives with his three boorish sons, only to announce that Ida locked herself away in Castle Adamant with a hundred girls, teaching them to renounce men and study.

Hilarion, who is in love with Ida, sets out to win her over with his friends Cyril and Florian, but through charms, not warfare. They disguise themselves as undergraduates and enlist the help of Florian's sister Lady Psyche, who is a professor at the university, and Melissa, a student who overhears them and is quite surprised that men are not as ape-like as the Princess would have them believe. Her mother Lady Blanche, another professor at the university, meanwhile hopes to use the marriage to take over Adamant and get rid of both Ida and her academic rival Psyche.

King Hildenbrand refuses to wait long, though - Gama and sons are locked in a dungeon to make certain that nothing happens to the prince and promises to storm Adamant's halls, should Ida not swallow her pride...

Hilarity Ensues, of course. It should be noted that this is a hard piece to sell to modern audiences, given the dated jokes about women's education.

Tropes used in Princess Ida include:

Affably Evil:

King Hildenbrand: You'll remain as hostage here, should Hilarion disappear, we will hang you - never fear! Most politely, most politely, most politely.

Arranged Marriage: Hilarion hopes it will turn out to be a Perfectly Arranged Marriage, being in love with Ida from the start. In the end, it seems to work.
Beta Couple: Cyril and Psyche, Florian and Melissa.
Bowdlerization: Lady Psyche, professor of humanities, advises her students to do this with classics. It can also be said for the whole play - the initial poem had Ida's brothers winning the duel against Hilarion and friends.
Bawdy Song: Tenor Boy Cyril gets one, while Disguised in Drag. In front of the whole university, members of which watch with astonishment and horror.
Childhood Marriage Promise: Minus the promise - they actually were married as children and thus have been married for twenty years, without ever interacting. Hilarion even sings a song about it.
Cloudcuckoolander: Ida, by the standards of the time, but her whole family is very odd.
Compassionate Critic: Gama provides the trope page quote and introduces himself with a song about it.
Cool and Unusual Punishment: Gama is horrified to learn that Hildenbrand intends to treat him with absolute luxury, meaning that complaining becomes impossible. He's in a misanthrope's hell: a place where there is never anything to complain about and everything suits him.
Crossdresser: Hilarion, Florian and Cyril disguise themselves as undergraduates when entering Castle Adamant. They even sing a trio about it - I am a maiden.
Deadpan Snarker: King Gama, (who was Gilbert's parody of himself!)
Disguised in Drag: Hilarion, Cyril and Florian.
The Ditz: The Three Brothers Arac Gurion and Scynthius qualify. They are so dumb after not taking their armor off for the entire piece they remove it all BEFORE GOING INTO BATTLE. Probably the only example of this trope in all of Gilbert and Sullivan.
Dumb Muscle: Ida's three brothers are... not smart. Bonus for the fact that they sing a song about it and openly admit it - they're not intelligent, but they're "warriors three".
Grande Dame: Lady Blanche
Gratuitous Iambic Pentameter
Opening Chorus:

Search throughout the panorama
for a sign of royal Gama
who today should cross the water
with his fascinating daughter
Ida is her name.

Grande Dame: Lady Blanche
Have a Gay Old Time
Honour Before Reason: Hilarion saves Ida from falling into a stream, but she still wants to punish him for his deception. When Hildenbrand's troops arrive, she refuses to surrender despite being egregiously outnumbered and loudly proclaims her intention to die rather than marry the fair, strong and tall (her own words) prince.
"I Am" Song: "If You Give Me Your Attention" for King Gama.
Lady of War: Ida is quite willing to fight Hildenbrand's entire army on her own, if need be. Subverted Trope: she never gets to do so.
Pair the Spares: Justified Trope - The girl scholars have been kept completely isolated from men, taught that they're like apes. Ooh, look, men have appeared! They decide to further their education.
Straw Feminist: The whole premise, basically.
Those Two Guys: Cyril and Florian.
Wig, Dress, Accent: Only Lady Psyche and Lady Blanche aren't fooled - the former is Florian's sister, so they let her in on it before she can expose them in any way and Blanche agrees to keep it quiet because Ida's marriage would be advantageous to her.