Please give a character analysis of Katharina in Shakespeare's The Taming of the Shrew, with quotes to support your analysis.
In Shakespeare's The Taming of the Shrew, Katharina is an ill-tempered, ill-mannered, nasty, and rude young woman of exceptional beauty, who refuses to be courted by any of the young men of the town.
In Act Two, scene one, Katharina has tied her sister up and demands to know who she likes best of all her suitors. When Bianca's answers do not please her, she slaps her sister in the face.
Of all thy suitors, here I charge thee, tell
Whom thou lovest best: see thou dissemble not. (8-9)
Bianca swears that no one man appeals to her any more than another.
Believe me, sister, of all the men alive
I never yet beheld that special face
Which I could fancy more than any other. (10-12)
Bianca denies than any man appeals to her. She offers her anything she owns (jewelry, clothes, etc.), and even is willing to speak on Katharina's behalf if she desires a certain young man. Katharina believes it is all a bunch of lies, and smacks Bianca just as her father is entering the room.
If that be jest, then all the rest was so.
Baptista is the father of the two girls; he enters, comforting Bianca and chiding Katharina, but his oldest daughter will not be corrected by her father and promises to have her revenge against Bianca.
Her silence flouts me, and I'll be revenged.
Katharina is also abusive toward the young men of the town who come to court her. However, Petruchio arrives from Verona and hears about Katharina. It seems that Baptista will not allow his younger and gentler daughter Bianca to marry until the nasty Katharina is wed. And Katharina is having nothing to do with this plan. Petruchio has come, he says, to find a wife. When he learns of Katharina whose father is offering a large dowry in marriage, but has a shrewish disposition, Petruchio ignores the warnings of those around him and promises that he will marry her for her money, unafraid of her ill-temper.
When Petruchio has made arrangements with Baptista to marry his oldest daughter, he asks Baptista to send Katharina to him. He addresses her, however, as "Kate." He speaks sweetly to her, trying to woo her, saying that she "moves" him. But as is her custom, Kate tells him to leave alluding that his is "movable"—like a piece of furniture, and nothing more:
Moved! in good time: let him that moved you hither
Remove you hence: I knew you at the first
You were a moveable.
Her insults continue—she infers that he is an "ass," among other things; but Petruchio is undaunted, eventually forcing her to marry him despite the hatred she exhibits toward him.
At the start of the play, Katharina seems a spoiled brat, but reading between the lines, I believe she is miserable because all the young men prefer her younger sister and her father (Baptista) favors Bianca as well.
… Nay, now I see
She is your treasure, she must have a husband;
I must dance bare-foot on her wedding day
And for your love to her lead apes in hell.
Talk not to me: I will go sit and weep
Till I can find occasion of revenge. (31-36)
Kate does not help her case by being so mean-spirited, but in a way, she may do so because acting nasty helps her to create a reason why the young men do not like her. She would rather believe it is her behavior that puts these men off, rather than believe it is because she is less worthy than her sister.