Petruchio is a cocksure gentleman who comes to Padua in seek of a wife, only to get more than he bargained for when he sets his eyes upon the strong-willed Kate. It is Petruchio's friend Hortensio who suggests he court Kate, whose wealthy family will provide a large dowry when she weds. Additionally, Hortensio is in love with Kate's sister Bianca, and she cannot herself get married until her older sister does first. Hortensio prevails on Petruchio to introduce him to the family as a music teacher for Bianca, so that he may secretly woo her. Another man, Lucentio, does the same, posing as a tutor.
Petruchio is struck by Kate's beauty, but also her temper. He responds to her every insult by acting as though she has praised him, and tells her father that she is only pretending to hate him. He convinces her mother that she has consented to the wedding. The two are married in a ceremony where Petruchio deliberately embarrasses Kate by arriving in a ridiculous outfit and riding a broken-down horse.
After the wedding, Petruchio whisks Kate back to his home, before the feast. He and his servants torment her by refusing to let her eat or sleep -- saying the food is not good enough for her, and the bedding is of too low quality for a woman of her refinement.
Lucentio wins Bianca's heart, and attempts to win the favor of her mother, but the older woman needs proof that Lucentio is a man of good fortune. Unable to do so, the lovers elope. At the same time, Petruchio and Kate are returning to Padua, her will nearly broken from days of mistreatment. In a gripping scene, he forces her to say the sun is the moon and make other obviously false statements, which she does.
When all return to Padua, those who knew Kate are shocked to see that she has been tamed by Petruchio, who makes a wager that his wife is more obedient than any other man's. He, along with Lucentio and Hotensio, calls his wife and orders her to do as he says, which Kate does. She then lectures the other wives on the importance of obedience to their husbands.
Best part of story, including ending:
It's hard to like a story that shows a woman beaten down by an overbearing husband, even if there is no overt violence and it's all played for laughs. Kate was more interesting before she married Petruchio.
Best scene in story:
Petruchio and Kate share verbal insults in the first scene where they meet. Their wits are as sharp as anyone else in Shakespeare's canon.
Opinion about the main character:
Petruchio is not only cocky and obnoxious, but ... well that's it, generally speaking. Modern theatrical interpretations of the play often have actors portray him with some self-awareness, but a surface level reading of the play does not endow him with this quality.