Here is a brief plot summary of The Taming of the Shrew:
The play opens as the student Lucentio arrives in Padua. He hears that the merchant Baptista has two daughters, but the younger, prettier daughter, Bianca, cannot be married before her strong-willed sister, Katherina. On seeing Bianca Lucentio falls in love with her and changes identities with his servant Tranio. Bianca already has two suitors, but doesn’t like either. The elderly Gremio hires Lucentio, disguised as a Latin tutor, to woo Bianca on his behalf, while Hortensio disguises himself as a musician to get access to her. Meanwhile Petruchio, a young adventurer from Verona, arrives to visit hisfriend Hortensio. He learns about Katherina and decides to woo her, aided by both Gremio and Hortensio.
Baptista is enthusiastic about Petruchio’s suit because the feisty Katherina is a burden to him and is continually quarrelling with her sister and with him. Petruchio will not be put off as he woos Kate and he fixes their wedding day. At the church, where Kate unwillingly awaits him, Petruchio arrives in an absurd outfit and after the ceremony he leaves for Verona immediately, with his new wife. On reaching there Kate is mistreated by Petruchio and his servants, and is denied food and sleep. To teach her to obey him Petruchio does not allow her new clothes or a hat. Eventually, worn down by her husband’s relentless eccentricity, Kate submits and accepts all his eccentricities. They set off to visit her father in Padua.
On the journey the couple meet Vincentio, Lucentio’s wealthy father, who is subjected to a strange conversation as Petruchio tests Kate’s obedience. The three reach Padua where Hortensio, rejected by Bianca, has married a widow and Baptista has been tricked into believing a passing stranger is Tranio’s rich father. While Vincentio attempts to unravel the complexities of the situation his son Lucentio returns from a secret wedding with Bianca.
Nevertheless, Baptista holds a wedding feast for both his daughters. As the men relax after their meal Petruchio devises a competition to prove whose wife is the most obedient. Bianca and the widow fail to come to their husbands when called while Kate lectures the women on the duties of a wife.