This play is thought of as Shakespeare's take on the battle of the sexes. Briefly, Lucentio arrives in the city of Padua keen to study, but then falls in love with Bianca, who already has two suitors and whose father, Baptista Minola, has declared that no one may marry Bianca until her older, foulmouthed sister, Katherine is married. Lucentio disguises himself as Bianca's Latin tutor to spend time with her. His friend, Petruccio, a brash young man, comes to Padua to find a wife - he doesn't care who she is as long as she is rich. He and Katherine meet and have an immense duel of words, ending in Petruccio telling Katherine that he will marry her whether she likes it or not and arranging the date with her father.
The wedding comes and Petruccio arrives late and dressed ridiculously. He then engages on a process of "taming" Katherine by depriving her of food and sleep. Lucentio in Padua finally wins Bianca's heart and her father agrees for them to marry for a price. Katherine and Petruccio return to visit her father, and we see that Katherine's wilfulness is fading fast. They agree to go to Lucentio and Bianca's wedding. After the wedding in a test of obedience everyone is shocked when Katherine wins it, and then gives a speech on loyalty to husbands.
Katherine at the start of the play is famed for her violence and illtemper and shrewish behaviour. She clearly does not fit well in to society, refusing to play her part of maiden daughter and also treating her suitors with respect and kindness. Yet, there is a paradox, because her only hope of fidning security is in a marriage, which arguably has led to her behaviour. We can see there is a bit of a vicious circle that has developed: the angrier she gets, the less likely it is she will be able to play her part in society; the more alienated she becomes in society, the more her anger grows.
We can see that in spite of the humiliation she suffers from Petruccio that in many ways he is well suited to marry Katherine. Their first conversation establishes him undoubtedly as her equal in intellect, temperament and character, and thus makes him very different from the normal suitors she is used to dominating. Petruccio's treatment of her shows her that she has no choice but to bow to society's demands and play the role of the wife. Katherine comes to realise that through playing this role she is able to speak with authority and command a respect that she is unable to do and command in her role as "shrew" and thus is tamed.