c. 1200, "a way, a road, space for passage," from Old French rute "road, way, path" (12c.), from Latin rupta (via) "(a road) opened by force," broken or cut through a forest, etc., from rupta, fem. past participle of rumpere "to break" (see rupture (n.)).
The sense of "fixed or regular course for carrying things" (originally and for long especially postal, as in mail route) is from 1792, an extension of the meaning "customary path of animals" (early 15c.) itself later extended to sales, collections, delivery of milk or newspapers, etc. OED says the pronunciation that rhymes with "stout" appeared early 19c.
1890, of a railroad ticket, "mark for use on a certain route," from route (n.). The meaning "direct (an electrical signal, phone call, etc.) over a particular circuit or to a particular location" is by 1948. Related: Routed; routing; routeing (1881).
c. 1300, "custom, habit," in phrase bi rote "by heart," a word of unknown origin, sometimes said to be connected with Old French rote "route" (see route (n.)), or from Latin rota "wheel" (see rotary), but OED calls both suggestions groundless. Meaning "a fixed or unchanging round," as in learning or reciting, is by 1580s. As a verb, "repeat, say from memory," 1590s.
"customary course of action; more or less mechanical performance of certain acts or duties," 1670s, from French routine "usual course of action, beaten path" (16c.), from route "way, path, course" (see route (n.)) + noun suffix -ine (see -ine (1)). The theatrical or athletic performance sense of "carefully rehearsed sequence of actions" is by 1926. The adjective, "of a mechanical or unvaried character, habitually done in the same way" is attested by 1817, from the noun. Related: Routinely.
"narrow track worn or cut in the ground," as by a passing wheeled vehicle, 1570s, probably from Middle English route "way, a road, space for passage" (see route (n.)); though OED finds this "improbable." If so, it is a doublet of route.
Of the lines on the face by 1620s. The figurative meaning "narrow, monotonous routine; habitual mode of behavior or procedure" is attested by 1839 (Carlyle); earlier figurative use was as an obstacle to rapid transit (1705).
Enter an OLD LADY.
[Bosola] You come from painting now.
Old Lady. From what?
Bos. Why, from your scurvy face-physic.
To behold thee not painted, inclines somewhat near
A miracle: these in thy face here, were deep ruts,
And foul sloughs, the last progress.
There was a lady in France, that having the small-pox,
Flay'd the skin off her face, to make it more level;
And whereas before she looked like a nutmeg-grater,
After she resembled an abortive hedgehog.
[Webster, "The Duchess of Malfi"]
The verb meaning "mark with or as with ruts" is by c. 1600. Related: Rutted; rutting.