Actors consider Hamlet to be a prize role; that complexity also makes him a good subject for research. The timeworn question of his "tragic flaw" draws on Aristotle's ancient writings on tragedy. Scholar James P. Hammersmith argues that this approach is misguided and simplistic. A more interesting paper would trace the idea of the tragic flaw from Aristotle through 20th century writer A.C. Bradley: Do you agree or disagree with the "tragic flaw" approach? Other topics include: Hamlet's relationship with his mother, which Ernest Jones' influential essay describes as "Oedipal," full of repressed sexual feeling; and his supposedly feigned madness, which may become actual madness. Indeed, scholars and legal experts have staged mock trials to determine whether Hamlet was insane during the play's action.
Surrounding the title character of Hamlet are a host of others, whose motivations and actions provide material to write about. His mother, Queen Gertrude, is a conflicting figure: How sympathetic is she? What is the nature of her relationship with her son? The other major female character, Ophelia, is one of the play's truly tragic innocents, and her madness and death provide a sadly ironic counterpoint to Hamlet's arguably pretend insanity. Her brother, Laertes, is a young man of action, often considered the classic foil, or literary contrast, to Hamlet.
Considering "Hamlet" as an exemplary tragedy will take you into the world of Aristotle's "Poetics," in which he sets out the features of a perfect tragedy. Specifically, "Hamlet" is a revenge tragedy, a popular genre at the time. The theme of revenge is key to the plot, as well as to the characters, so a research paper could fruitfully explore the nature of revenge and the effects of revenge on the people involved.
A play is never "just" a written text, but is intended to come to life on stage. The performance history of "Hamlet" is full of famous names, both men and women, and comparing two of the recorded performances can be a fascinating research project. The University of Hawaii's 2010-2011 season Audience Guide to the play gives a few suggestions of famous Hamlets. Each actor brings a unique vision to the role: What does each performance suggest about what kind of person Hamlet is? How does the overall scenery and setting affect the mood and tone of the play?