After Baptista breaks up a fight between Bianca and Katherine, the group of suitors and tutors arrive, and Petruchio gets right to the point, telling Baptista that he would like to court Katherine. He also introduces Hortensio, who is disguised as a music teacher named Litio. Not to be outdone, Gremio butts in to tell Baptista that he, too, has brought a tutor for Bianca—Cambio (who is really Lucentio in disguise). Then Baptista notices the stranger, Tranio, who introduces himself as Lucentio, adding that he’s yet another suitor for Bianca.

After and Baptista and Petruchio conduct the financial negotiations for his marrying Katherine, Hortensio (as Litio) returns with a broken lute after trying to teach Katherine how to play it. Baptista offers to take Litio to tutor the more gentle Bianca, and he tells Petruchio that he’ll send Kate out to meet him.

Left alone, Petruchio talks about his strategy for courting Kate, saying he’s going to ignore her bad temper and praise her instead. When she arrives, Kate is as disagreeable as everyone would expect her to be, but Petruchio attempts to court her nonetheless, describing her in glowing terms, as he told us he would. The courtship dance between them goes on for quite some time, and it’s hard to tell if they’re fighting or if they’re somehow made for each other. But it ends with Petruchio declaring that the two of them will be married.

Baptista returns with Gremio and the fake Lucentio. To everyone’s confusion, including Kate, Petruchio announces that he and Kate have agreed to get married. Since Kate is now engaged, Gremio and the fake Lucentio start to plead their cases with Baptista. They compete to see who can offer Bianca more wealth and possessions. Tranio (as Lucentio) outbids Gremio, so Baptista says Lucentio can marry Bianca, but only if Lucentio’s father, Vincentio, agrees. Tranio is left to figure out how to find a fake Vincentio to make those promises so that he can keep the lie going and win Bianca’s hand for his master, Lucentio.