Vladimir Propp

In Morphology of the Folktale (1928), Vladimir Propp tries to define the components of a tale and the relationships of these components to each other and to the whole.

From Morphology of the Folktale, trans. Laurence Scott (Austin & London: University of Texas Press, 1968), pp. 19-21:

"What methods can achieve an accurate description of the tale? Let us compare the following events:
1. A tsar gives an eagle to a hero. The eagle carries the hero away to another kingdom.
2. An old man gives Súcenko a horse. The horse carries Súcenko away to another kingdom.
3. A sorcerer gives Iván a little boat. The boat takes Iván to another kingdom.
4. A princess gives Iván a ring. Young men appearing from out of the ring carry Iván away into another kingdom [...]

Both constants and variables are present in the preceding instances. The names of the dramatis personae change (as well as the attributes of each), but neither their actions nor functions change. From this we can draw the inference that a tale often attributes identical actions to various personages. This makes possible the study of the tale according to the function of its dramatis personae.
[...]
Function is understood as an act of a character, defined from the point of view of its significance for the course of the action. The observation cited may be briefly fromulated in the following manner:
1. Functions of characters serve as stable, constant elements in a tale, independent of how and by whom they are fulfilled. They constitute the fundamental components of a tale.
2. The number of functions known to the fairy tale is limited."

Propp identified 31 functions, such as:

Absentation (one of the members of the family is absent from home. "An intensified form of absentation is represented by the death of the parents")

Interdiction (an interdiction or order is addressed to the hero)

Violation (the fulfillment of the command implies a violation or misfortune)

Villainy (the villain causes abducts or imprisons a person / causes bodily injury)

Lack (the hero lacks something or desires to have something)

First function of the donor (the hero is tested... which prepares his way for receiving either a magical agent or helper)

Pursuit (the hero is pursued)

Rescue (of the hero from pursuit)

Return (of the hero)

Exposure (the false hero or villain is exposed)

Punishment (the false hero or villain is punished)

Wedding (the hero is married and ascends the throne)