The relationship between Hamlet and his father has its difficulties, but from Hamlet's first soliloquy we can see that he idolizes his father: "So excellent a king, that was to this/Hyperion to a satyr". He compares his father to Hyperion to illustrate his beauty, power and love for Gertrude, although he had no knowledge of his character, of his believes because of their estranged relationship. The king was a weak father that never spent time with his son due to his military obligation (Hamlet's father: an analysis of paternity and filial duty in Shakespeare's Hamlet; by Justin Dathan Anders Drewry, 2004). .
Their relationship can be analysed from two perspectives. Firstly from Hamlet's childhood and adolescence, when, as I mentioned before he lacked of a parental figure and secondly after the death of King Hamlet, who has come back from Purgatory (as it is believed by the prince, even if he was a protestant) to revenge his death through his son. The Ghost is not very easy to assimilate for everyone, especially for Hamlet, who feared in the beginning as we see in these lines: "Angeles and ministers of grace defend us!/ Be thou a spirit of health or goblin damned." Hamlet, Bernard, Horatio are not willing to think evil of the king, and they all want some undoubted proof not only of the fact of the ghost's appearance, but of the truth of his words. But all of Hamlet's doubts are finally removed in the fourth scene when he sees the ghost for himself and learns the ugly truth: "A serpent stung me, so the whole ear of Denmark/The serpent that did this sting thy father's life/Now he wears his crown." At last, the evidence overcomes his moral reluctance to believe such foul suspicions, and Hamlet is convinced of the guilt of the actual king, Claudius, his uncle.
Now all he has to do is fulfill his father's request of revenging him:" Revenge his foul and most unnatural murder.