Reading points: some matters to consider as you read:
Hamlet as a "revenge tragedy" (genre based on the Roman Seneca); Hamlet as Aristotelian tragedy?
Illusion in conflict with reality: what seems to be vs. objective "truth." Misperception vs. intentional deception. Rampant irony!
The importance of family, different familial relationships and responsibilities.
Court politics, political intrigue, "politician-like behavior."
The burdens of leadership.
Imagery of nature, health, corruption, and sickness.
Uncommonly frequent religious overtones (for Shakespeare, that is).
Metadrama: more commentary upon art and/or theatrical drama through "players" and a "play within the play."
Reasons for Hamlet's indecision.
Foils, characters that are "like but unlike," characters who mirror or "twin" with one another.
Thematic significance in scenes of comic relief: connections between adjacent scenes.
The question of whether we do or do not fully identify or sympathize with Hamlet.
The play's continuing relevance: significant applicability in a number of respects to modern readers.