The various suitors of Bianca hatch their plans.
Characters: 
Lucentio

Lucentio arrives in Padua to study, but soon gets distracted by Bianca.

Tranio

Lucentio's servant helps him hatch a plan to woo Bianca in disguise. 

Baptista

The father of Katherina and Bianca wants to marry off Katherina before he'll let the suitors court Bianca. 

Gremio

The elderly suitor wants to find a husband for Katherina so that he can court Bianca. 

Katherina

Baptista's oldest daughter is famously disagreeable, making her an undesireable candidate for marriage. 

Bianca

Baptista's appealing youngest daughter has many suitors, but can't be courted until Katherina is married. 

Hortensio

The suitor wants to find a husband for Katherina so that he can court Bianca. 

Biondello

Biondello is confused to find his master Lucentio and his other servant, Tranio, have swapped roles. 

First Servant

Sly's servant wonders if Sly is paying proper attention to the play.

Sly

Sly attends the play with his lady (who is really the lord's page).

Page

The lord's page attends the play with Sly, acting as his lady.

Scene Summary: 

Act 1, Scene 1 begins the play that’s performed for Sly. The play is set in the Italian city of Padua, where a young nobleman, Lucentio, and his servant, Tranio, have just arrived. Lucentio has come to Padua to study virtue and philosophy. Just after they arrive, they eavesdrop on a nearby conversation. Baptista, a local nobleman, is explaining to two other noblemen, Gremio and Hortensio, that his youngest daughter, Bianca, can’t be courted for marriage until his oldest daughter, Katherine, is married. But Gremio and Hortensio find Katherine to be incredibly disagreeable, so they’re only interested in marrying Bianca. Baptista asks the two suitors for help finding music and poetry teachers for his daughters, as a way for them to spend their time until Katherine gets married. After Baptista and his daughters leave, Hortensio gets Gremio to agree that the best way forward is to find a husband for Katherine so that they can get back to courting Bianca.

Meanwhile, Lucentio has fallen head over heels in love with Bianca from afar, and Tranio has to remind him that it’s not going to be easy to court her, because the other daughter needs to be married first. But then they both get the same idea: Lucentio can pretend to be a schoolmaster and act as Bianca’s tutor, while Tranio pretends to court Bianca as Lucentio. The two swap outfits. A second servant of Lucentio’s, Biondello, shows up, and he’s immediately confused by the change of clothes. Rather than tell him what just happened, Lucentio makes up a story that he killed somebody and needs to be disguised in order to escape, and so Biondello agrees to play along.

The scene ends with a servant asking Sly how he’s liking the play so far. Sly says he thinks it’s excellent, but he clearly wishes it were over already.