In terms of literature, what is the Formalist theory?
Formalism is a school of literary criticism that separates a work from the influences of culture, authorship, and society or politics; that is, a work is analyzed purely on its own intrinsic worth. Along with Structuralism, Formalism emerged when science and sociology took on importance in the early part of the twentieth century. In a sense, then, the Formalist theory calls for the analysis of a work of literature's composition and structure, the mechanics of the literary work such as genre and the inherent features such as the syntactical structure and the use of literary devices such as symbol, tropes, meter, rhythm, figures of speech (especially in poetry).
In a novel such as Fitgerald's The Great Gatsby, for instance, a Formalist approach to this work would include how the author juggles time (as part of the element of setting) in the telling of the background of Jay Gatsby; it would also analyze Fitzgerald's marvelous use of symbols and imagery and the trope of recapturing the past. On the other hand, this approach would ignore the tableau of the Jazz Age that Fitzgerald so craftily presents in this novel and the portrayal of the Eastern society with its hierarchy as reflective of the historical period in which the work is set. Also, when Fitzgerald inserts popular songs from the Jazz Age, such as "Three O'Clock in the Morning," a Formalist criticism would not include a discussion of how this song is reflective of the culture of the Roaring Twenties; instead, it may discuss how this song reflects a mood.
Statements by characters would be analyzed simply on their own merit. For instance, when Nick Carraway calls Daisy and Tom Buchanan "careless people," a Formalist criticism would analyze how the Buchanans are selfish and unfeeling toward others, not caring what happens to others:
They were careless people, Tom and Daisy--they smashed up things and creatures and then retreated back into their money or their vast carelessness or whatever it was that kept them together, and let other people clean up the mess they had made.
However, other types of criticism would include the observation that Nick's epithet for the Buchanans also implies that they do not care what is done to others so long as they have their social position and reputation intact (societal analysis). Thus, they typify the wealthy socialites of the East that Fitzgerald himself so disliked (authorship analysis).