Here is a brief plot summary of The Taming of the Shrew:
A wealthy Padua merchant, Baptista, has two daughters. One day Lucentio, a student, comes to Padua, sees Bianca, the younger sister, and falls madly in love with her. He has heard, though, that Baptista will not allow Bianca to be married before her older sister, Katherina, a very forceful character who has a scornful attitude to men and expresses that without restraint. The situation regarding Bianca is very complicated and Lucentio’s entry into the equation makes things even more complicated. Two local men, Hortensio and the elderly Gremio, are pursuing Bianca but she doesn’t like either of them so they have to resort to a range of tactics to try and further their interest. Gremio hires Lucentio, disguised as a Latin tutor, to woo Bianca on his behalf. Hortensio poses as a musician to try and get into her company.
While all this is going on Petruchio, a young friend of Hortensio from Verona, pays a visit to his friend and hears the story about the feisty Kate. He sees her as a challenge, which he decides to rise to. Baptista welcomes this as he is fed up with Kate’s disruptive behaviour, that makes family life difficult. He accepts Petruchio’s offer of marriage and although Kate opposes it, she cannot do anything about a father’s right to marry his daughter off. Petruchio arrives at the church outlandishly dressed and whisks her off to Verona as soon as the marriage is pronounced. During the journey, Kate rebels against her husband but he begins training her to obey him. On arrival at his house, Petruchio mistreats her and instructs his servants to do the same. She is denied everything she wants for a civilised life, including food and sleep. She is not allowed new clothes or any luxury. That wears her resistance down and eventually, she submits and becomes an obedient wife.
It is time to visit her father where Petruchio plans to demonstrate his wife’s obedience.
In the meantime Hortensio has given up on Bianca and married a widow. Lucentio and Bianca, having fallen in love, have run off and married secretly. They return now, while Petruchio and Kate are visiting and Baptista, relieved that it’s all turned out better than he had thought it would, hosts a party for his daughters. They all have a good time and as the men gather together after the meal Petruchio challenges Lucentio and Hortensio to a competition to see which of their wives is the most obedient. Each one is to command his wife to come to him. Bianco and the widow fail to respond whereas Kate does and, furthermore, delivers a lecture to the other wives on the duties of a wife.