In the story, it isn't enough for Montresor to simply exact revenge on and kill Fortunato. He has a very specific idea of what this revenge must entail. He says, "A wrong is unredressed when retribution overtakes its redresser. It is equally unredressed when the avenger fails to make himself felt as such to him who has done the wrong." Thus, Montresor cannot incur any punishment as a result of his revenge, and he must make it known to Fortunato that it is he, Montresor, who is responsible for Fortunato's fate. If he is punished somehow or fails to make his responsibility known to his victim, then he will consider the revenge null. This, for Montresor, his revenge is a point of pride. It is his pride, personal and even familial, that has been wounded, and so he feels that he must avenge those wounds in order to maintain his honor. Only pride would require him to make his role in Fortunato's fate known to the man before his death. Therefore, pride is a major theme in this story as well.
In addition to pride, this story explores the nature of guilt. Montresor tells his tale to someone who "know[s] the nature of [his] soul" some "half of a century" after the events occurred. Thus, it stands to reason that he is now an old man confessing his sins to a priest (someone who would know his soul). If the sin has burdened him for so long, then did he really exact his revenge without punishment? Some would argue that he has not. Is guilt punishment enough to negate his completion of his revenge? The story thus takes guilt as another of its themes.