In Act I Sc. V of Hamlet, the ghost of Hamlet's father speaks to Hamlet.
The ghost tells Hamlet to do three things.
a) The ghost informs him that he was not killed by a snake bite, as most people were led to believe, but rather was killed by his brother Claudius, who now is married to Hamlet's mother and is King. The ghost tells Hamlet to revenge this "most foul, strange, and unnatural" murder.
This task is, of course, the one that Hamlet hesitates to do throughout the play.
b) The Ghost says to Hamlet that he should not let his "soul contrive(90)
Against [his] mother aught." In other words, he should do no harm to his mother, even though she has acted treacherously by marrying her husband's murderer.
c) Before the Ghost leaves, he says to Hamlet, "Remember me." The meaning of this phrase is debatable. Is it a new directive, in which the Ghost commands Hamlet to always revere his memory? Or is the Ghost just telling Hamlet that he should remember to carry out the instructions that he has already given him?
In Act I, Scene V, of Hamlet, the ghost tells Hamlet to avenge his death. The ghost reveals himself as Hamlet's recently deceased father and claims to be the victim of a "foul and most unnatural murder." He tells Hamlet that the story of his death, as told by his uncle, is completely false: a snake did not bite him while he slept in the orchard. In truth, Hamlet's uncle crept upon him as he slept and poured a vial of poison into his ear. The poison got quickly to work, leaving the king no time to repent of his sins. As a result, he is now trapped in a horrible place called purgatory.
After the ghost leaves, it becomes clear that his plea for revenge has been successful. Hamlet refers to his uncle as a "villain" and his mother as "pernicious." In short, Hamlet's mind can think of nothing but revenge.
The Ghost tells Hamlet 3 things:
1. revenge his foul and most unatural murder
2. taint not thy mind... nor contrive against thy mother aught
3. remember me (the father's spirit)