How does Shakespeare present women in The Taming of the Shrew?

The Taming of the Shrew is set in Italy in the late 1500s, and suggests that women should be mild-mannered, and obedient to their husbands. In the play, Shakespeare contrasts the two main female characters, Katherina (a.k.a. Kate) and her sister Bianca. The two sisters are very different from each other - while Bianca is calm and obedient, Kate is fiery and self-assertive. Bianca is seen as the ideal woman in the play. Her 'mild behaviour' (I.i.72) is an attractive quality for a potential suitor, and so she has lots of men wanting to marry her. However, Kate and Bianca's father has decided that Bianca cannot get married until Kate has been wedded. His daughters must obey him because, in Shakespeare's society, women were seen as the property of their father until they were married, when they became their husband's property instead. This indicates that Shakespeare presents his female characters as being controlled by men. Kate's refusal to submit to male control puts off a lot of men from marrying her, until a character called Petrucchio decides that he wants to 'tame' her. This is what the title refers to - a 'shrew' was a word for an angry, disobedient woman in Shakespeare's time. Petrucchio 'tames' Kate by refusing to give her food or allowing her to sleep, saying that his intention is to 'kill [his] wife with kindness' by 'curb[ing] her mad and headstrong humor' (IV.ii.208-09). Petrucchio also makes Kate agree with everything he says to prove her obedience to him, even asking her to say that the sun is actually the moon. Kate, suffering from lack of food and sleep, responds by saying 'Then God be blessed, it is the blessed sun, / But sun it is not when you say it is not, [...] What you will have it named, even that it is, / And so it shall be still for Katherine.' (IV.vi.19-20, 22-23). This shows that even though she doesn't really believe that the sun is the moon, she has realised that her only option is to go along with what Petrucchio says is true in order to save herself from suffering more. Eventually, at the end of the play, Kate has been worn down by Petrucchio's control and in the final scene proves herself to be the most obedient wife out of three women. She gives a long speech on why women should obey their husbands, whom she claims are their 'lords, kings and governers' (V.ii.154). It is debateable whether Kate has actually changed her mind about her role as a woman, or whether, having suffered under Petrucchio's control, she is using her cunning to use her position to her advantage. Either way, The Taming of the Shrew suggests that the only way for women to behave in Shakespeare's society is to be meek, and submit to male authority. Bianca embodies these qualities throughout the text, but Petrucchio and Kate's relationship shows that even the most headstrong woman in the play can be tamed into obedience. The Taming of the Shrew therefore seems deeply misogynistic by modern standards, but can tell us a lot about views of women in Shakespeare's time.