At Castle Adamant, Princess Ida’s pupils learn that “man is nature’s sole mistake” (Towards the Empyrean heights). One of the Professors, Lady Blanche, doles out the punishments for the day, for “offences” that include bringing chessmen to the university — “men with whom you give each other mate” — and for sketching a double-perambulator. Princess Ida arrives (Minerva! Oh hear me) and delivers a stern lecture, stating that women’s brains are larger than men’s, and predicting that woman shall conquer man, but that once having conquered, woman will treat man better than he has treated her. Lady Blanche resents the Princess and predicts that one day she will replace her as head of the university (Come Mighty Must, a song often cut from the D’Oyly Carte productions).

Hilarion, Cyril and Florian sneak into Castle Adamant (Gently, gently). They scoff at the idea of a woman’s college. Finding some discarded academic robes, the three men disguise themselves as young maidens wishing to join the university (I am a maiden cold and stately) and are welcomed by Princess Ida (The world is but a broken toy). Florian realises that their disguises won’t fool his sister, Lady Psyche (one of the professors), and they take her into their confidence. Lady Psyche warns them that they will face death if the Princess discovers who they are and informs them of the Princess’s theories on man, using a parable about an ape who falls in love with a high-born lady to illustrate her point that Darwinian “Man, sprung from an Ape, is Ape at heart” (A lady fair of lineage high).

Melissa, Lady Blanche’s daughter, has overheard them, but, fascinated by the first men she has ever seen, swears herself to secrecy. She falls in love with Florian at first sight, and the company celebrate joyously the discovery that men are not the monsters that Princess Ida had claimed (The woman of the wisest wit). Lady Blanche, who has not fallen for the men’s disguises, confronts Melissa. Though indignant at first, she is persuaded to keep the men’s secret when her daughter points out that if Hilarion is able to woo Princess Ida, Blanche will become head of the university (Now, wouldn’t you like to rule the roast?).

During lunch (Merrily rings the luncheon bell), Cyril gets tipsy and inadvertently gives away his friends’ identity by singing a bawdy song (Wouldn’t you know the kind of maid). In the ensuing confusion, Princess Ida falls into a stream, and Hilarion rescues her (Oh joy, our chief is saved). Despite her rescue, Ida condemns Hilarion and his friends to death. Hilarion counters that without her love to live for, he welcomes death (Whom thou hast chained). King Hildebrand and his soldiers arrive, with Ida’s brothers in chains. He reminds her that she is bound by contract to marry Hilarion and gives her until the following afternoon to comply (Some years ago) or incur the guilt of fratricide. The defiant Ida replies that, although Hilarion saved her life and is fair, strong, and tall, she would rather die than be his bride (To yield at once to such a foe).