The relationship between Hamlet and his mother, Gertrude, is a complex and troubled one. Throughout the play, Hamlet grapples with his feelings towards his mother, who he sees as complicit in the murder of his father, the late King of Denmark. This causes a great deal of conflict and tension between the two characters, as Hamlet struggles to come to terms with his mother's actions and to understand her motivations.
At the beginning of the play, Hamlet is deeply troubled by the news of his father's death and the quick remarriage of his mother to his uncle, Claudius. He is disgusted by the fact that his mother could move on so quickly from the death of his father and marry his uncle, who is now the King of Denmark. Hamlet feels that his mother has betrayed his father's memory and that she is complicit in the murder of the King. This creates a great deal of resentment and anger towards his mother, and Hamlet struggles to reconcile these feelings with his love for her.
Despite this tension, Hamlet does try to understand his mother's actions and motivations. He realizes that Gertrude may have been under a great deal of pressure to marry Claudius, as he was the most powerful man in the kingdom and she may have feared for her own safety. Hamlet also recognizes that his mother may have had feelings for Claudius and that she may have truly believed that she was doing the right thing by marrying him.
Despite these considerations, Hamlet cannot fully forgive his mother for her actions. He is deeply hurt and disillusioned by her betrayal of his father, and he struggles to come to terms with this betrayal. This struggle ultimately leads to Hamlet's tragic end, as he is unable to fully resolve his feelings towards his mother and is consumed by his own grief and anger.
Overall, the relationship between Hamlet and his mother is a complex and troubled one. It is marked by conflict, resentment, and a deep sense of betrayal, as Hamlet struggles to come to terms with his mother's actions and to understand her motivations. Despite this, however, Hamlet does try to understand his mother and to reconcile his feelings towards her, and it is this struggle that ultimately leads to his tragic end.