Comment on the context in which William Shakespeare wrote his play; Hamlet. How is it relevant to themes of justice and revenge within the film?
any relevant additional information is greatly appreciated
What do you mean by "context"? There is an historical context, religious context, literary context, philosophical context, political context, etc. Since your questions also refer to justice and revenge, I might assume that you are referring to the political or historical context, or religious context, correct? If this is not correct, please re-post your question and be more specific.
During the middle ages and beyond, monarchs were seen as being God's representatives on earth and having what was referred to as "divine right of rule." Unfortunately, most monarchs abused this power and the power was unchcked. Killing a king, however, was a very, very big deal, so Hamlet's hesitation to kill his uncle is understandable. That is why the murder of King Duncan in Macbeth is also very odious. So the political context of Hamlet is that it was written most likely while Queen Elizabeth I was still the reigning monarch in England. She happened to be one of the monarchs that actually cared about her people, so Hamlet's hesitation and moral ambiguity in avenging his father's death is significant. This is often underestimated by modern readers who believe Hamlet was weak because he hesitated so long before taking action against Claudius.
The other significant "context" to this play would be religious. During Elizabethan times, people believed that vengeance belonged to God, not man, and that any vengeance carried out by man had to be in accordance with the will of God, or God-ordained. Again, Hamlet is troubled by his conflict over justice and revenge - he seeks justice, but is it up to him to avenge his father's death? Should he leave that up to God? Notice that Hamlet does not want to kill Claudius while he is praying because he fears that Claudius might go to heaven if he dies while in prayer (a mis-interpretation of Christianity, however).
If this is not what you are seeking, please re-post your question.