Who is Sly and what is his purpose in the play?(question from induction of play)
I'm sure you mean Christopher Sly. First of all, Sly provides a frame for the main story of Kate and Petruchio. He is a drunkard who is thrown out of the tavern. Some lords think would be funny to pull a practical joke on him when he awakens from his drunken stupor. They take him home and when he awakens, he is treated as a lord. He is asked what clothes he would like to wear, what music he would like to hear, when he would like to go hunting. They also bring him a page dressed like a woman who is supposed to be Sly's wife. Pretty funny stuff, eh?
It doesn't take Sly long to become persuaded that he is indeed a lord, and begins watching the play (Taming of the Shrew), while he is "recovering" enough to have sex with who he thinks is his wife.
In many ways, the ideas in Christopher Sly story are picked up in the main story. Ideas about identity, pretense, courting--male/female relationships, and transformations are common to both stories. And, when we watch Katherine and Petruchio spar and Bianca flirt with her suitors, we must remember that we are seeing this play through the eyes of the drunkard tinker Christopher Sly.