What are the theories of The Merchant of Venice?
What is it precisely that you mean by "theories"? Are you refering to the themes that can be identified in this play and used to analyse it? Or do you mean various approaches such as gender, race and ethnicity that can be used as metaphorical keys to cast new light on the action of this play.
If it is themes you are after, I have included a link below to the enotes study section on themes of this play. If you are after theories, you might like to consider considering how examining the concept of gender can be used to interestingly challenge male patriarchy and the perception of the relations between the sexes.
One can easily see the significance of approaching this play through the lense of gender by examining the characters of Jessica and Portia. Let us remember that it is Jessica who, of her own accord, organises her escape from her father's somewhat grim and unhappy household, stealing his wealth while she was escaping. Lorenzo follows her orders in this and is presented as being rather stupified by the gain of both a wife and significant wealth. The initiative is taken by Jessica. In the same way, let us remember that it is Portia who saves her new husband's best friend in the light of his inability to do anything to save him. Act IV scene 1 is fascinating for many different reasons, but one of the reasons is the way that Bassanio is portrayed as standing helpless on the sidelines whilst his wife, in disguise, shows how extremely capable she is and that she can more than deal easily with situations that leave her husband baffled and helpless. Gender is subverted to present women as stronger and more powerful figures than men, which is very interesting given the patriarchal society in which Shakespeare was writing.