How does Shakespeare's presentation of the female characters in Hamlet further his purposes?
Gertrude and Ophelia are presented as weak women subject to the various actions of men. Throughout the drama they react, rather than act with resolve or firm moral determination. Ophelia's suicide might seem to be an action born of determination, but it is really a reaction to all she has endured in her male-dominated young life.
These female characters in their weakness serve several purposes in the play. First, through them the plot is advanced. Gertrude's seduction by Claudius sickens and infuriates Hamlet, further pushing him into avenging his father's murder. Through his relationship with Ophelia, the daughter of Polonius, Hamlet plants the first seeds to suggest that he has gone mad, an integral part of his plan to discover the truth about his father's death. Additionally, it is Ophelia's death that drives Laertes into the plot with Claudius to kill Hamlet.
Also, in his relationships with these two weak women, Hamlet's complex character is more deeply developed. He is appalled by his mother's behavior, but he loves her and tries to save her from further acts of debasement; his relationship with her intensifies his torment. His relationship with Ophelia further torments him. He uses Ophelia in his plot against Claudius, but in doing so, he deliberately pushes her away while loving her deeply. Ophelia's death causes Hamlet great agony.
Gertrude and Ophelia are important in the drama not for the women they are but for the passive roles they play in Hamlet's tragic destruction.