Bianca and Lucentio are falling in love.
Characters: 
Tranio

Tranio, in disguise as Lucentio, helps Hortensio-as-Litio spy on Lucentio-as-Cambio, and later convinces the Merchant to act as Lucentio's father. 

Hortensio

Having given up on winning Bianca, Hortensio reveals himself to Tranio. 

Lucentio

Lucentio makes progress wooing Bianca, and later convinces a Merchant to pose as his father. 

Bianca

Bianca is falling in love with Lucentio.

Biondello

Biondello brings good news: he's found someone to pose as Lucentio's father. 

Merchant

The unsuspecting Merchant gets duped into pretending to be Lucentio's father, for fear of his life. 

Scene Summary: 

At the Minola household, the fake tutor, Litio (AKA Hortensio), is complaining to the fake Lucentio (AKA Tranio) that Bianca seems to be flirting with the other tutor, Cambio. He wants Tranio, who he thinks is Lucentio, to spy on them with him. Just then, Cambio and Bianca pass by in the middle of a Latin lesson, and it definitely looks like they’re falling for each other. His suspicions confirmed, Hortensio takes off his tutor disguise and tells the fake Lucentio that he’s going to forget Bianca and marry a rich widow instead.

When Hortensio leaves, Tranio joins Bianca and Lucentio to tell them that Hortensio no longer wants to marry Bianca. Biondello arrives to announce that he’s spotted a merchant approaching the town who might be a candidate for a fake Vincentio—someone to play Lucentio’s father and make financial promises to Baptista. When the merchant arrives, the Tranio-as-Lucentio convinces him that his life is in danger, but then offers him a way to protect himself by pretending to be Lucentio’s father, Vincentio. Fearing for his life, the merchant agrees, and then Tranio adds the little detail that the fake Vincentio will have the job of promising money to Baptista for Lucentio’s marriage to Bianca.