How does Shakespeare explore the theme of revenge within ‘Hamlet’?

Hamlet's reluctance towards revenge and his need for it's confirmation is in contrast to the irrationality which comes with revenge, 'for there is nothing either good or bad but thinking makes it so - to me it is a prison.' Hamlet is obviously imprisioned by his thoughts, which is ironic since the only way for him to be free of prison is to commit a crime. He feels an obligation to avenge his father's 'foul and unnatural murder' so that he may not 'fast in fires.' All sins must be purged in order for the late king to go to heaven, meaning that he is stuck in purgatory until they are, a fate considered worse than hell in Elizabethan times.