The first sentence indicates that we have a first-person narrator:
The thousand injuries of Fortunato I had borne as best I could; but when he ventured upon insult, I vowed revenge. You, who so well know the nature of my soul, will not suppose, however, that I gave utterance to a threat.
The first-person narrator in this case is Montresor, and as with all first-person narrators, the reader can only understand the story's events through the eyes of one person. Although we can see into the narrator's character, mind and soul, we are limited to the narrator's perceptions of the world around him, inlcuding the nature of all the other characters in the story. In "The Cask of Amontillado," therefore, we have a first person limited narrator--limited in the sense that we can only see through his eyes.
One of the enduring problems with Montresor-as-narrator, though, is that the reader can never be sure of Montresor's reliability as a narrator. After all, we have a man who constructs a horrific murder for a man--Fortunato--who has apparently insulted Montresor. Because Montresor never identifies what the insult is, most readers ask the same question, "What did Fortunato do to deserve such a fate?" One reasonable conclusion is that Montresor is unbalanced by his desire for revenge, and many readers decide that Montresor is a first-person unreliable narrator.
The question of Montresor's state-of-mind, then, becomes a central issue in this story simply because readers are never sure whether they are seeing the story's events as they actually occur or as a twisted mind recounts the events. Montresor's unreliability creates a problem of belief that has haunted readers and literary critics for almost two centuries.