Hamlet, Dimitri Tavadze (2013), CC BY-SA 3.0 <https://creativecommons.org/licenses/by-sa/3.0>, via Wikimedia Commons
(left) "My Father's House" by Bruce Springsteen (1982)
Although not directly tied to Hamlet, I found this song on a playlist titled "the tragedy of hamlet" ~ take it or leave it, just some interesting resonances I noticed.
(right) "To Billy or not to Billy" from Billy Madison (1995)
This rendition of the beginning of Hamlet's "to be or not to be" monologue melodramatizes this moment for the purposes of comedy, and is far from anything I would expect us to want to channel in this production. But I actually find it quite useful in guaging potential audience expectations/underlying assumptions regarding this play and the portrayal of Hamlet himself. If the audience is expecting something like intense melodrama in this moment, how do we manage those expectations?
The Death of Hamlet, Eugène Delacroix (1843), CC0, via Wikimedia Commons
A typical revenge play features a protagonist whose actions are motivated by, you may have guessed it, revenge. One of the features of Shakespeare's revenge tragedies (Titus Andronicus is a key example of this) is the circularity and retributive nature of revenge: the revenger never escapes the consequences of their revenging action. Generally, these consequences include death.
The genre of a revenge play is grappled with throughout Hamlet, most notably by Hamlet himself. Plays like The Spanish Tragedy and The Revenger's Tragedy share certain features with Hamlet, but this play is unique in its commitment to self-questioning. After being instructed by the ghost to avenge his death by killing Claudius, Hamlet finds himself caught up in the plot to a story he doesn't want to be a part of, let alone the star. As such, he stalls and reflects and questions his actions before commiting to them: a very anti-revenge tragedy protagonist.
Folger Shakespeare Library (1900), CC BY-SA 2.0 <https://creativecommons.org/licenses/by-sa/2.0>, via Wikimedia Commons
Hamlet and Ophelia, Dante Gabriel Rossetti (1853), Public domain, via Wikimedia Commons
The role of providence, or divine mandate, in Hamlet is an extremely active question. Hamlet himself consistently asserts his own free will over the ghost's otherworldly demands, a maneuver that mirrors the skepticism burgeoning in Renaissance-era England. Full fledged atheism was still viewed as a misguided inner feeling on the road to salvation, but the Elizabethan national religion of Protestantism did allow for a more nuanced understanding of doubt and "unbelief" than the Catholic church. Combined with an increasingly educated middle-class, religious doctrine was something to contend with rather than simply accept.
That said, the threat of temptation and devilry was still quite active. Hamlet's trepidation around the ghost would be seen as quite reasonable to audiences at the time: the devil could use such tricks to convince otherwise devout Christians to commit sinful deeds.
Hamlet, Michele Rapisardi (1886), Public domain, via Wikimedia Commons
Hamlet, Bibliothèque nationale de France (1946), Public domain, via Wikimedia Commons
The precarity of Hamlet's political position stems from him being the heir apparent to Hamlet Sr., a position particularly threatening to Claudius' reign. As the only other viable candidate for the throne, he represents a problem that Claudius must contend with to secure his position. He is a prince, the (original) heir apparent to the throne, but Claudius has not only wronged him personally (by killing his dad and marrying his mom) but politically as well by sweeping him aside in the line of succession and (should Gertrude have children with him) pushing him out of contention for the throne altogether.
Hamlet has been a feminized figure throughout much scholarly discourse of his conduct in the play. His overall sensitivity, hesitance to inflict violence, and emotional distress/grief over his father's death are all traits that run counter to ideals of hegemonic masculinity.
These two articles/book chapters offer interesting gendered accounts of Hamlet's behavior in the play. First, The Woman in Hamlet: An Interpersonal View, is a late 70's psychoanalytical account of Hamlet's behavior, viewing his relationships to the other characters through the intensely family-rooted Freudian view of relationships. I would recommend skimming it, start on page 293 (I believe this cuts to the quick of Hamlet's isolation and is the least jargon-y part of the paper). Then, Gender Tragedies: East Texas Cockfighting and Hamlet is an autobiographical account of the expectations of masculine performance that I find to be particularly interesting and potentially helpful for excavating the nuances of Hamlet's relationship to his father. To get into the meat of that argument, start on page 72.