Reading points: a few matters to consider as you read:

Psychological complexity and depth in characterization; consider especially how Katharina and Petruchio are interesting and challenging roles for actors.

 Illusion vs. reality: in particular, note how many different characters become "actors" and play assumed roles in front of different "audiences."
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 Thematic parallels between the induction scenes and the "play proper."

 Parallels or intersections of theme or meaning between the two primary plots (centering on Katharina and Bianca respectively): consider how these two plots inform or "comment upon" one another.
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 Shakespeare's humor: consider different comedic techniques or different types of humor.

 Petruchio's "taming" method: Shakespeare's apparent commentary upon gender.

 Open to interpretation: consider ways this seemingly patently sexist play may be interpreted from other, less sexist perspectives. Look for gender-centered passages that may be read in entirely different tones.

 The evolving relationship between Katharina and Petruchio: from possible initial attraction to love?  Do they end up really in love?  Is this play a legitimate "romantic comedy"?

 The play's continuing popularity: why does this play have such staying power?

 The play's continuing relevance: any significant applicability to modern readers?