Kate's only suitor and future husband, Petruchio is an amazing character that on the surface appears to be rough, noisy, and insensitive - a person who cares nothing for Katherine's feelings so long as she has money. Yet, in the inside Petruchio's intention is not interested for her money but the challenge of capturing her because of the reputation that she has. He manages to "kill her in her own humor" (IV.ii. 180) by taking the same physical and methods in use as she did. He teaches Kate happiness through reversed psychology.
The transformation that Kate undergoes near the end of the play is not one of character, but one of attitude. Her final speech in the very end of the play clearly displays that she has changed and that she's willing to accept the role as a married woman and start a partnership with her husband. She submits herself by stereotyping women as physically weak and then suggests that they should make their personality mild to match their physique: "Why are our bodies soft, and weak, and smooth... But that our soft conditions and our hearts should well agree with our external parts?" (V.ii.169172).
A crucial factor in the "taming" of Katherine in The Taming of the Shrew is definitely the societal values of the day. Back in medieval Europe there was no doubt who was the boss at home and women were expected to fulfill the role as the housekeeper and stay at home: "Thy husband is thy lord, thy life, thy keeper, thy head, thy sovereign..." (V.ii. 150-151). Back in the day this ranking, this hieracy, wasn't questioned, which is why Katherine is such a revolutionary character, especially in relation to the contemporary time the play was written.
When The Taming of the Shrew first was performed no one had in mind that William Shakespeare could've thought ahead of his time, by bringing up the idea of sexual equality. Whether that really was his purpose of writing this play or not,...