Literary devices are of two categories: literary elements and literary techniques. Literary elements are common to all fiction in one form or another. Literary techniques are options each individual author can choose from and therefore vary between literary works.
In The Strange Case of Dr. Jekyll and Mr. Hyde, one example of a literary element is the narrator, or narratorial voice. The story starts with a third person limited narrator who tells the story through Mr. Utterson's experience, thoughts, motives, and feelings. Other literary elements to consider are conflict; rising action, climax, falling action, resolution, all part of plot structure; character development (direct or indirect); foreshadowing; setting; point of view; mood; tone; and theme.
One literary technique (optional choice of author) in the story is Stevenson's use of epistolary sections. In Chapter 9, Dr. Lanyon takes over as the narratorial voice by means of his letter to Mr. Utterson. Further, in the beginning of Lanyon's epistle (letter) is an embedded letter to Lanyon from Jekyll. So Lanyon's letter to Utterson consists in part of a letter quoted inside a letter. Chapter 10 is given over to Jekyll's narratorial voice again through the literary device of an epistolary (literary) technique as Utterson reads Jekyll's letter, his confession, addressed to himself, Mr. Utterson.
Some other literary techniques to look for are allusion, symbolism, metaphor and simile, metonymy, puns, personification, irony (verbal, situational, dramatic), idiom, flashback, and cliche.
The Strange Case of Dr. Jekyll and Mr. Hyde uses images of light and dark to stand for the evil of Mr. Hyde and the goodness of Dr. Jekyll. For example, as Mr. Utterson is making his way to Dr. Jekyll's apartment, he encounters fog and darkness in the following passage: "And at last his patience was rewarded. It was a fine dry night; frost in the air; the streets as clean as a ballroom floor; the lamps, unshaken, by any wind, drawing a regular pattern of light and shadow." These images of light and shadow stand for the contrast between Hyde and Jekyll, and the pattern of shifting light and darkness suggests the connection between them.
The book also includes figurative language, such as the simile in the following example: "so that the shop fronts stood along that thoroughfare with an air of invitation, like rows of smiling saleswomen." In this example, the shop fronts are compared to salespeople who invite the passerby into the store.
The book also includes symbols. For example, the doctor's cabinet, a room in which he encloses himself, is a symbol of the recesses of his mind. In the following passage, the doctor hides himself in his cabinet:
"The doctor, it appeared, now more than ever confined himself to the cabinet over the laboratory, where he would sometimes even sleep; he was out of spirits, he had grown very silent, he did not read; it seemed as if he had something on his mind."
The doctor's cabinet stands for the secrets of his mind, in which he encloses himself. Mr. Utterson's attempts to visit Dr. Jekyll in his cabinet symbolize Utterson's attempts to understand Dr. Jekyll and what he is thinking.