Frankenstein is what's known as an epistolary novel, its narration told through epistles or letters. Samuel Richardson perfected the form in his influential Pamela, Or, Virtue Rewarded (1740), in Clarissa, Or, The History of a Young Lady (1748), and then, turning from a female to a male protagonist of superior virtue, Richardson wrote The History of Sir Charles Grandison (1753). But it is probably Goethe's The Sorrows of Young Werther, which plays a central role in the monster's education, that infuenced Mary Shelley.
The epistolary form avoids an omniscient narrator and relies on personal expression by an immediately concerned correspondent, becomes importan to what's called the sentimental novel or novel of sensibility. These works focus upon a person of an especially sensitive temperamen who is quick to express sympathy and emotion in general.
Richardson's subject matter and psychological exploration shape novels by Henry Mackenzie, Fanny Burney, Mrs. Radcliffe, and Austen. Grandison was a favorite of George Eliot (Mary Ann Evans). As suggested above, one of the most influential epistolary novels was Goethe's The Sorrows of Young Werther (1774; Search).
At first, Frankenstein's letters are brief, but as we proceed they lengthen until we forget we're reading a letter.