What is the theme of "The Cask of Amontillado" by Edgar Allen Poe?
You asked more than one question so I have edited your question to focus on this excellent gothic short story. Clearly a central theme that goes to the very heart of this excellent short story is that of revenge. From the very first paragraph it is clear that revenge is Montresor's central motive for acting in the way that he does:
The thousand injuries of Fortunato I had borne as best I could; but when he ventured upon insult, I vowed revenge.
Although the exact nature of this "insult" is never divulged, revenge is the driving force that leads Montresor to plot and enact his most gruesome of punishments. Consider Montresor's motto, "Nemo me impune lacessit", which means "Nobody attacks me without punishment", which adds a moment of black humour to the story as Fortunato responds to the firmness of this motto with a strong approbation: '"Good!" he said.' Of course, the first paragraph is key to the reader in terms of displaying Montresor's plan, which is an enactment of his motto:
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.
It is vital therefore to Montresor that Fortunato meets his fate at his hand - Fortunato must know that it is Montresor who is exacting the revenge himself, otherwise, by Montresor's definition, it would not be revenge.
Of course, the fact that the short story never makes it clear precisely what the grevious offence was that plagues Montresor so does beg the question of whether Montresor is entirely reliable - of course, if Fortunato had wronged Montresor so badly it would be unlikely that he would trust Fortunato enough to follow him by himself into the depths of his family catacombs.
Hopefully this will help you work out the theme for other short stories you are studying as well, by using this as an example.