The Taming of the Shrew is a play within a play by Shakespeare. It's a story told by a man, Sly, in an alehouse in England, and his story is set in Padua, Italy - in a public square, in Baptista's house, and in Lucentio's house. Other scenes take place in Petruchio's country house and on the road between there and Lucentio's house. Read more about The Taming Of The Shrew settings. Date written: 1592 Genre classification: The Taming of the Shrew is a comedy play. Main characters in The Taming of the Shrew: The action revolves around Katherine (Kate), the daughter of Baptista and the older sister of Bianca. Katherine has no suitors because she is not conventionally attractive but more seriously, she is notoriously shrewish, and seems to hate men, which makes it difficult for any man to deal with her. Bianca is sweet natured and beautiful but can't marry until her older sister does.