At the beginning of Hamlet, by William Shakespeare, Hamlet is distraught about two things: his father's untimely death and his mother's untimely marriage. Gertrude's role in this play, either as complicit or innocent in the murder of her husband, is one which prompts great debate, as does the nature of her relationship with Hamlet. Many of the things that she says and does in the play are a matter of interpretation. 

In the first scene Hamlet and Gertrude have together, she suspects he might possibly be upset by her "o'erhasty marriage," but she also wants him to stop mourning so dramatically--perhaps because it makes her feel a bit guilty. While he does not yet know that Claudius murdered King Hamlet, Hamlet knows that his father was a far superior man to Claudius; he says they are like Hyperion (one of the Titans) and a satyr (lecherous half-man and half-goat). Hamlet is clearly upset with her choice of husband, but he is also furious with her for being weak ("Frailty, they name is woman!") and marrying someone so quickly after seeming, at least, to love her husband so dearly. Instead of drawing them closer, King Hamlet's death has created an obvious rift between them, as Hamlet says, "But break, my heart; for I must hold my tongue."

As the play progresses, Hamlet seems to have enacted his plan to put on an "antic disposition," and Gertrude is worried again that her hasty marriage to Claudius may be the cause; Claudius fears that Hamlet knows the truth but does not share that with Gertrude. When Polonius proposes his plan to send Ophelia as bait to Hamlet so they can listen to their conversation, Gertrude eagerly agrees. This does not seem like the action of a caring mother, though she may actually just be desperate to know what is really causing her son's madness.

When she calls Hamlet to her chamber, Gertrude's plan is to be stern with him and find out what is wrong. Instead, Hamlet is rather ruthless in his condemnation of her choice in husbands and soon Gertrude is asking what she can do to make it right. In the middle of this exchange, however, the Ghost makes his appearance, and only Hamlet can see or hear it. Perhaps Gertrude admits her failing because she thinks she is to blame for Hamlet's apparent madness or to appease her son in his madness. 

In any case, she agrees not to tell Claudius that Hamlet is only "mad in craft"; as soon as she sees Claudius, she tells him that Hamlet killed Polonius and is

Mad as the sea and wind, when both contend

Which is the mightier....

Whether she was breaking her promise or helping Hamlet continue his charade is a matter of interpretation--has Gertrude now allied herself with Claudius or Hamlet?

In the final scene, things seem good between mother and son, and for once Gertrude does not listen to her husband when he tells her not to drink. Though this small act eventually kills her, it does suggest that perhaps Gertrude has allied herself more with Hamlet than with her second husband. 

The relationship between Gertrude and Hamlet is complicated, and it is difficult to know the truth because of Hamlet's emotional state (grief, anger, perhaps madness) and Gertrude's possible dissembling about her husband's murder and her relationship with Claudius. While the relationship ends in destruction, it may not be the fault of the relationship but the outside forces at play in this tragedy.