You may remember that allusions may refer to previous literary works, mythology -particularly Greek myth- historical characters, or Biblical stories and characters.
In Hamlet, they begin to appear very early. Already in Act I, scene i, l. 33, Horatio says, "A little ere the mightiest Julius fell [...]" He is speaking of Julius Caesar, in a passage in which he describes the portents that Rome experienced before Caesar's murder. This passage establishes a comparison between such portents and the sighting of the Ghost. In Horatio's view, perhaps the Ghost is a harbinger of some impending catastrophe that will befall Denmark just as Julius Caesar's death proved disastrous to the Roman Republic.
In Act I, scene v, l.114, the Ghost says "[...] that roots itself indeed on Lethe wharf." The Lethe is one of the four rivers of the Greek underworld. Its particular characteristic is that, once the souls of the dead have drunk its waters, they forget their past as living creatures. In the context of the passage, the Ghost is telling Hamlet that only a creature who has been affected by the Lethe would remain "dull" (not take action) after listening to the story of treachery that ended up in the Ghost's murder.
It is generally understood that the Ghost is Hamlet's father come from the dead. However, as postmodern critique challenges this on the basis of applied psychoanalysis, I am intentionally refraining from taking the Ghost's identity for granted.
I hope this helps.