rut (n.1)

"narrow track worn or cut in the ground," 1570s, probably from Middle English route (see route (n.)); though OED finds this "improbable." Metaphoric meaning "narrow, monotonous routine; habitual mode of behavior" first attested 1839.

rut (n.2)

"annually recurring sexual excitement in animals; animal mating season" (originally of deer), early 15c., from Old French rut, ruit, from Late Latin rugitum (nominative rugitus) "a bellowing, a roaring," from past participle of Latin rugire "to bellow," from PIE imitative root *reu-. The verb is recorded from early 15c. Related: Rutting.

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Definitions of rut from WordNet
rut (n.)
a groove or furrow (especially one in soft earth caused by wheels);
rut (n.)
a settled and monotonous routine that is hard to escape;
they fell into a conversational rut
Synonyms: groove
rut (n.)
applies to nonhuman mammals: a state or period of heightened sexual arousal and activity;
Synonyms: estrus / oestrus / heat
rut (v.)
be in a state of sexual excitement; of male mammals;
rut (v.)
hollow out in the form of a furrow or groove;
Synonyms: furrow / groove