Let's examine the two major themes that drive Shakespeare's 'The Taming of The Shrew'.
The play is ultimately about finding a suitable partner for marriage. The motivations for marriage in the play vary enormously, however. Petruccio is only really interested in marriage for economic gain. Bianca, on the other hand, is in it for love.
Lucentio has gone to great lengths to win Bianca's favour and to get to know her better before committing to marriage. He disguises himself as her Latin teacher in order to spend more time with her and to gain her affections. However, Lucentio is only permitted to marry Bianca because he has managed to convince her father that he is incredibly rich.
Had Hortensio offered Baptista more money he would have married Bianca despite her being in love with Lucentio. Hortensio settles for marriage to the widow after his marriage to Bianca is refused. He would rather be married to someone than have no one.
It is usual in Shakespearian comedies that they end in marriage. The Taming of the Shrew does not end with a marriage but observes several as the play goes on.
Moreover, the play considers the impact that a marriage has on family members, friends and servants and on how a relationship and bond is formed thereafter.
There is a form of elopement where Bianca and Lucentio go off and marry in secret, a formal marriage between Petruccio and Katherine where the social and economic contract is key, and the marriage between Hortensio and the widow which is less about wild love and passion but more about companionship and convenience.
Theme: Social Mobility and Class
The play is concerned with social mobility which is ameliorated through marriage in Petruccio's case, or through disguise and impersonation. Tranio pretends to be Lucentio and has all the trappings of his master while his master becomes a servant of sorts in becoming a Latin teacher for Baptista's daughters.
The Local Lord at the beginning of the play wonders whether a common Tinker can be convinced he is a lord in the right circumstances and whether he can convince others of his nobility.
Here, through Sly and Tranio Shakespeare explores whether social class is to do with all the trappings or something more fundamental. In conclusion, one could argue that being of high status is only of any use if people consider you are of that status. Vincentio is reduced to a 'faded old man' in Petruccio's eyes when he is encountered on the way to Baptista's house, Katherine acknowledges him as a woman (who could get any lower on the social strata?).
In fact, Vincentio is super powerful and rich, his social status is what convinces Baptista that his son is worthy of his daughter's hand in marriage. Social status and class are therefore very important but transient and open to corruption.
Katherine is angry because she does not conform to what is expected of her by her position in society. She tries to fight against the expectations of her family, friends and social status, her marriage ultimately forces her to accept her role as wife and she finds happiness in finally conforming to her role.
In the end, the play dictates that each character must conform to his position in society. Tranio is restored to his servant status, Lucentio back to his position as a rich heir. Katherine is finally disciplined to conform to her position. In an additional passage to the play even Christopher Sly is returned to his position outside the alehouse having been stripped of his finery:
Go take him easily up and put him in his own apparel again and lay him in the place where we did find him just underneath the alehouse side below.
(Additional Passages Line 2-4)
Shakespeare suggests it is possible to cheat class and social boundaries but that the truth will win out and one must conform to one's position in society if we are to live a happy life.