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One of the things I noticed right away was not just the humor, but where the humor was coming from. When Viola disguises herself as a eunuch, and then is described as feminine and compared to women, we get situational humor. The same holds true for when Olivia falls in love with Viola. But there are characters in the play who are just funny, as well. Sir Toby is a drunk, and much of what he says is comical. He plays on words and has Andrew dance for him, but is still able to say profound things: "What dost thou mean? Is it a world to hide virtues in?"
Then there is the Fool. He is just returning from a trip and needs to get into Olivia’s good graces. The first thing that happens is not in his favor:
Olivia. Take the Fool away
Fool. Do you not hear fellows? Take away the Lady.
I laughed at this part, but he goes on to explain how Olivia really is being a fool for her prolonged mourning.
Meanwhile, Orsino is pining after Olivia. And it seems to be all he does, despite Olivia’s rejections. The play seems to point out how love is what makes people foolish, not the usual things, like being drunk or actually being a Fool. This comparison of love and foolishness is fascinating. For further research I would look up articles that have probably been written about the subject, but also I might look at other plays by Shakespeare that have similar tones. I would especially look at his other comedies to see if they might have similar themes that Shakespeare liked to explore.
I'll mention one more direction I could go in my research. "Twelfth Night" includes a lot of pagan symbols, which doesn't strike me as odd in a story full of deception. It reminds me somewhat of some of those old greek mythological stories. I might look into the images used in the play and see how they relate to the mythology.