Courtship: disguise and dowries
Getting married seems to be no easy thing to do in The Taming of a Shrew. Grumio and Hortensio both disguise themselves as teachers in order to get close enough to Bianca to talk to her, while her father says that he will not allow her to be married* until her older sister, Katherine, is married.
The authority of fathers in the Renaissance.
The sub-plot of the wooing of Bianca by her various suitors in disguise is very similar to the plots of the Roman New Comedy, where an old man (the senex) objects to the marriage of the young lovers, but is outwitted by a clever servant.
Fortunately for Bianca's suitors, Petruchio comes to woo Katherine. Initially, however, his desire to wed Katherine comes from his desire for money* . This arrangement suits Baptista fine, as he is willing to give a large dowry for whoever will take the unruly Katherine -- and does his best to ensure that Bianca will marry a weathy man.
Getting married in the Renaissance.
Footnotes
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Oldest first
Baptista, Katherine's father, says that he has decided "not to bestow my youngest daughter / Before I have a husband for the elder" (1.1.50-51).
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Mercenary Petruchio?
Petruccio says, upon arriving in Padua, "I come to wive it wealthily in Padua; / If wealthily, then happily in Padua" (1.2.72-73).