A good thesis statement or topic sentence gains the reader's attention and is a promising beginning for an argument. It should focus on a particularly intriguing, outstanding, or puzzling element in the story for which your essay will offer a convincing reading. In the case of "The Cask of Amontillado," one of the aspects which most shocked contemporary readers was the lack of justice at the end of the story. Montresor is never punished for his hideous crime. You might, therefore, have a topic sentence which looks something like the following:
In "The Cask of Amontillado," Poe subverts the idea that crime does not pay.
Another interesting approach would be to focus on Montresor's state of mind. He talks about the "thousand injuries" Fortunato has inflicted upon him but gives no examples, while Fortunato himself does not seem conscious of any animosity. Your topic sentence in this case might argue...
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that
Fortunato is innocent, and Montresor is insane.
You might also think about the circumstances in which Montresor is making this confession (which, in his case, is more like a boast). He drops a few hints, saying that his listener knows him well and that it is fifty years since the events he describes. He also shows great pride in his cleverness. It may be that Montresor is now on his deathbed and beyond the reach of justice or that he is writing this down for someone to find after his death. You might use a thesis statement discussing how Montresor views his murder of Fortunato not as a crime for confession but as a work of art which he must reveal to the world before he dies.
Based on the final part of the question, it seems that you are asking for help writing an introductory paragraph about “The Cask of Amontillado.” The start of that introductory paragraph is your “attention getter,” and the end of the paragraph will be your thesis statement.
The thesis is a critical part of the introductory paragraph; however, I always emphasize to students that the first sentence is equally important. The first sentence is what must grab reader attention. You can have the best thesis in the world, but if your first sentence leaves your reader bored, he/she might not even bother reading long enough to get to your thesis statement.
Since you are writing a paper about a piece of literature, I recommend one of four attention-getters.
Use a quote. This is preferably from “The Cask of Amontillado.” A quote carries extra weight and importance in the minds of most readers. Using a quote activates reader engagement because the reader believes the quote is of critical importance.
Use a definition. Preferably the definition will have something to do with your thesis statement. If your thesis is about about revenge, maybe you could define revenge.
Make a bold, perhaps controversial, statement. The goal here is to get an emotional response out of your reader. “Fired up” readers keep reading.
Ask a question. This is probably the easiest attention getter. It will guide the opening paragraph because you will hopefully answer it within the following sentences. Additionally, a question immediately forces your reader to consider possible answers to the question. That kind of reader is an engaged reader, and he/she is likely to keep reading.
To close the introductory paragraph, you will use your thesis statement. A good thesis statement is a statement that is debatable. Your paper’s goal is to prove your thesis. Saying that “The Cask of Amontillado” is a story about revenge is not a thesis. There isn’t anything to debate. I usually recommend a two-part thesis statement. The first part of the statement admits to the counterargument of the second part of the statement. You can easily start this kind of thesis with the word “although.” For example: “Although readers generally assume that Fortunato is Montresor’s first victim, it is much more likely that Montresor has killed before and will kill again.” That particular thesis allows you to closely examine Montresor’s motivations for killing Fortunato and closely examine his extremely well-executed plan.
I think if I were going to write a paper about "The Cask of Amontillado" I would start out with a sentence somewhat like this:
In Edgar Allan Poe's story "The Cask of Amontillado," the narrator, a man named Montresor, describes the necessary components of a perfect revenge and then tells a supposedly true story of how he succeeded in accomplishing an act of revenge to his own complete satisfaction.
Then I would pretty much repeat what the narrator says about a perfect revenge and try to describe how he carried out his intended murder of his friendly enemy Fortunato. I suppose I would conclude with some words about how the revenge must have been successful because Montresor says that no one has discovered the body in fifty years.
Poe wrote at least one other story in which he began with a generalization and then told a tale to illustrate it. This was his equally famous story "The Murders in the Rue Morgue."