A Marxist analysis of Othello should include a discussion of the class divisions in Othello’s world. Focus on the motivations for the characters’ behavior and the causes of the conflict between them. Othello is a member of the upper class, and Iago is a member of the working class, and Iago is angry at Othello for denying him a promotion and giving it instead to a person of means. Iago embodies the working-class struggle to get ahead, despite the subjugation by the ruling class. He strives for personal advancement, but he is also the victim that responds in a society that institutionalizes oppression. Thus, his actions reflect learned behavior in an unjust and materialistic world.
A psychoanalytical analysis of Othello could focus on the propensity for destructiveness, both in Othello and in Iago. You might discuss whether their destructiveness is the result of trauma or whether it is instead, an instinctive response. Both characters suffer rejection and both exhibit anger and aggressiveness. You might explore whether their responses and reactions are the result of narcissism, and to what extent their failures reflect insecurities they feel about their power and about their desirability in love.