Bianca urges Katherine to allow herself to be wooed and to get married lest her shrewishness condemn Bianca to be confined and sequestered unto eternity. Consequently, under the pretext that Bianca is lying when she denies she is neither partial to Hortensio or Gremio, Katherine beats Bianca. By and by, Baptista scolds his elder daughter for roughing up her innocent younger sister, prompting Katherine to complain and weep that her father is partial to Bianca.
Alone, Baptista wonders what will become of him and his daughters when guests arrive. Among them, Petruchio distinguishes himself by announcing his intention to woo Katherine and by introducing the musician Litio (Hortensio in disguise) who, Petruchio assures, will make an ideal tutor for Baptista’s daughters. Baptista welcomes Petruchio as well as Gremio who introduces Baptista to Cambio (Lucentio in disguise), a young scholor of Greek and Latin who, Gremio assures, will make an ideal tutor for Katherine and Bianca. As for Tranio, he introduces himself as Lucentio, the son of the famed merchant Vincentio, and informs Baptista that he has come to woo Bianca.
Presently, the tutors are conveyed to Baptista’s daughters, and despite Baptista’s warning of Katherine’s temper, Petruchio repeats his intention to woo and wed Katherine. Suddenly, Litio (Hortensio in disguise) appears in a state of disarray. He tells of how he has been beaten by Katherine when he tried to teach her how to play the lute. Consequently, Baptista has Litio attend to Bianca and goes to fetch Katherine for Petruchio who is eager to meet her.
When Katherine appears, Petruchio calls her Kate and compliments her in every way. Naturally, Katherine, who only has insults for Petruchio, objects to being called Kate. But Petruchio insists on calling her Kate, absorbs her every insult with equanimity, and even permits himself to be struck without retaliating. Petruchio continues to speak highly of Kate when Baptista appears with Gremio and Tranio. Protesting that her father would allow a lunatic to woo her, Katherine leaves in a huff. Undaunted, Petruchio argues that Katherine is only pretending to be cross and that in reality the two of them are in the best of terms and assures Baptista that he will marry Katherine on Sunday.
Pleased with Petruchio’s resolve, Baptista turns his attention to his younger daughter Bianca’s situation. By and by, Gremio asserts that he is Bianca’s man which Tranio, acting the role of his master Lucentio, disputes. Baptista assures the suitors that deeds rather than words will win her daughter. Subsequently, Gremio enumerates his wealth, which will be Bianca’s, only to have his offer superseded by what Lucentio has to offer Bianca. Baptista agrees that Lucentio’s dower is the greater, and provided that Lucentio’s father Vincentio gives consent to Lucentio’s stated intention, Baptista offers Bianca to be Lucentio’s betrothed. Otherwise, if Lucentio's father denies Lucentio his promise, Bianca will be Gremio’s betrothed.
Arguing that Lucentio’s father wouldn’t consent to give up his wealth to his son just yet, Gremio assures Lucentio that Bianca may yet be Gremio’s betrothed when all is said and done. Alone, Tranio, commends himself for doing all he can on his master’s behalf and resolves to continue doing all he can on his master’s behalf.