Here's the breakdown:
* Hamlet is the Prince of Denmark, the son of the late King Hamlet and Queen Gertrude.
* Queen Gertrude is the current Queen of Denmark, having married Claudius, her late husband's brother, after his death.
This family dynamic is a key element of the play's central conflict, as Hamlet struggles with his grief for his father and his disgust at his mother's hasty marriage to his uncle, whom he believes murdered his father.