Petruchio arrives in Padua, while the suitors hatch their plans.
Characters: 
Petruchio

Petruchio arrives in Padua looking for a wife, and quickly agrees to pursue Katherina, undeterred by her famous shrewishness. 

Grumio

Petruchio's servant has accompanied him to Padua, and offers humorous commentary on the scene's events. 

Hortensio

Hortensio greets his friend Petruchio, and decides to disguise himself as Litio, a music teacher, so that he might court Bianca. 

Gremio

Bianca's suitor arrives with Cambio (Lucentio in disguise), a schoolmaster he intends to offer to Baptista as a tutor for Bianca.

Lucentio

Lucentio has disguised himself as Cambio, a schoolmaster, so that he might get closer to Bianca. 

Tranio

Tranio, disguised as Lucentio, is on his way to Baptista's house to court Bianca on behalf of his master.

Biondello

Biondello accompanies Tranio-as-Lucentio, acting as his servant. 

Scene Summary: 

Petruchio, and his servant, Grumio, who have also just arrived in Padua, head straight to the house of Petruchio’s good friend, Hortensio. Petruchio tells Hortensio that he’s traveled to Padua to seek his fortune and to find a wife. Hortensio tells him about Katherine, the rich but disagreeable daughter of Baptista. Petruchio says he’s not afraid of a scolding woman, and the fact that Katherine is rich is reason enough to marry her. He’s ready and willing to go meet Baptista. Hortensio wants to go with him, but he’ll disguise himself as a music teacher so he can sneak his way into Baptista’s household to woo Bianca.

Just then, Signor Gremio passes by with Lucentio, who has tricked Gremio into thinking he is a schoolmaster named Cambio. Hortensio tells Gremio the good news: Petruchio is willing to court and marry Katherine, no matter how disagreeable she is. Tranio, disguised as Lucentio, shows up with Biondello and asks for directions to Baptista’s house, saying that he wants to court Bianca, too. Petruchio points out that Katherine needs to be married before anybody can court Bianca, but that he’s willing to be the one who courts Katherine first. Because they can’t compete for Bianca’s hand in marriage until Katherine gets married, Gremio, Hortensio, and Tranio (as Lucentio) all agree to act like friends and get a drink together.