Describe how Macbeth's character changes throughout the play Macbeth?
In Shakespeare's Macbeth, before Macbeth kills Duncan, his thoughts are only on achieving the throne for himself. He gives no thought to the prediction by the witches that Banquo's heirs shall be king. Once he is crowned, though, his own kingship is no longer enough. His ambition has deepened and at that point he wants to create a dynasty. Thus, he orders the murder of Fleance, Banquo's son, for no other reason than to eliminate Banquo's heirs.
Macbeth also begins to rely on the witches more heavily after he kills Duncan and is crowned. He even initiates contact and seeks them out in Act. 4.1. Following his visit to the witches, he becomes even more intent on maintaining power, throwing almost what could be described as a tantrum when he can't get Macduff, because Macduff has gone to England. Macduff slights Macbeth by not attending his coronation or his feast, and Macbeth pays him back by ordering the slaughter of Macduff's family. This overreaction demonstrates Macbeth's loss of perspective and control as the play continues.
At the same time, the Macbeth of Act 5 is at once rash and contemplative and philosophical. One minute he childishly and maliciously berates a messenger, and the next minute contemplates human existence and becomes nihilistic. He psychologically moves back and forth between believing the witches and knowing their predictions are too good to be true, and between being willing to fight for his crown and die nobly, and knowing whatever he does is meaningless anyway.
In addition to the very useful observations already posted about Macbeth, there is the possibility of regarding him as a classic Tragic Hero, meaning he has a tragic flaw. In many Tragedies, the Hero suffers from hubris or excessive pride -- Odeipus and King Lear being two examples. This inflated sense of self leads to their downfall. The interesting thing about Macbeth, is that though he begins the play hesitant and fearful (afraid of the dagger that he sees before him and of the ghost of Banquo), he develops into a rather conventional Tragic Hero who considers himself invincible to defeat.
In Act V, Scene v, as he prepares to meet Malcolm and Macduff he says:
...our castle's strength
Will laugh a siege to scorn. Here let them lie
Till famine and the ague eat them up....
I have almost forgot the taste of fears.
The time has been my senses would have cool'd
To hear a night-shriek....I have supp'd full with horrors.
Direness, familiar to my slaughterous thoughts
Cannot once start me.
So he has indeed become hardened, and with this hardening he has also adopted the tragic flaw that will his downfall, overconfident hubris.
Over the course of the play, Macbeth's character goes from being more hesitant to overly ambitious and greedy. At the beginning of the play, Macbeth does not entirely believe the witches' prophecy and only does so once he becomes the Thane of Cawdor. Once he believes in the verity of the prophecy, he starts to think about how he will become king. Lady Macbeth persuades him to murder King Duncan to ensure his place on the throne; however, Macbeth wavers in this plan and is not sure whether or not it is the right thing to do. Lady Macbeth chides his manhood, and thus convinces him to proceed with the murder. After Macbeth becomes king, he allows his ambition and greed to consume him. He is fearful that his title will be taken from him, so he resorts to murdering all those whom he feels might get in his way. By the end of the play, Macbeth realizes that he has made the wrong decisions, yet he stands by them and fights until the very end.
Macbeth and Lady Macbeth are round, dynamic characters. What makes them such is because they both change from the beginning of the play to the end, and ironically, they seem to adopt the original characteristics of the other. Lady Macbeth is strong and masculine at the beginning of the play, expressing how she would murder her own baby to keep her promises, encouraging Macbeth to kill King Duncan by challenging his masculinity. Macbeth, on the other hand, has a conscious, and deliberates over the morality of killing the king. When Macbeth finally takes the dagger in his hand and does the bloody deed, he begins to change into a long spiral downward until he views life as "creep[ing] from day to day." Lady Macbeth, on the other hand, begins to develop a conscious, and she suffers from nightmares and boughts of sleepwalking that eventually lead her to commit suicide from guilt.