Etymology
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Words related to learn

*lois- 

Proto-Indo-European root meaning "furrow, track." 

It forms all or part of: delirious; delirium; last (n.1) "wooden model of a human foot used by shoemakers;" last (v.) "endure, go on existing;" learn; learning; Lehrjahre; lore.

It is the hypothetical source of/evidence for its existence is provided by: Latin lira "furrow;" Old Prussian lyso "field bed;" Old Church Slavonic lexa "field bed, furrow;" Old High German leisa "track," Gothic laistjan "to follow," Old English læran "to teach."

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last (n.1)

"wooden model of a human foot used by shoemakers," from Old English læste "shoemaker's last," earlier last "track, footprint, footstep, trace," from Proto-Germanic *laisti- (source also of Old Norse leistr "the foot," Middle Dutch, Dutch leest "form, model, last," Old High German leist "track, footprint," German Leisten "last," Gothic laistjan "to follow"), related to Old English læran "to teach," from PIE root *lois- "furrow, track."

learned (adj.)
"having knowledge gained by study," mid-14c., past-participle adjective from learn (v.) in its former transitive sense. Related: Learnedly; learnedness. "[L]earned expresses depth and fullness in the knowledge, while scholarly expresses accuracy" [Century Dictionary].
lere (v.)

OE læran, Kentish leran "to teach" (cognate with Old Frisian lera, Old Saxon lerian, Dutch leeren, Old High German leran, German lehren "to teach"), literally "to make known;" see lore). From early 13c. as "to learn."

learning (n.)
Old English leornung "study, action of acquiring knowledge," verbal noun from leornian (see learn). Meaning "knowledge acquired by systematic study, extensive literary and scientific culture" is from mid-14c. Learning curve attested by 1907.
learnable (adj.)
1620s, from learn + -able. Related: Learnability.
learnt 
occasional past tense and past participle of learn.
Lehrjahre (n.)
1865, from German Lehrjahre, from lehren "to learn" (see learn) + Jahre "years" (see year (n.)).
lore (n.)

Old English lar "learning, what is taught, knowledge, science, doctrine; art or act of teaching," from Proto-Germanic *laisti- (compare Old Saxon lera, Old Frisian lare, Middle Dutch lere, Dutch leer, Old High German lera, German Lehre "teaching, precept, doctrine"), from PIE root *lois- "furrow, track;" compare learn.

teach (v.)

Old English tæcan (past tense tæhte, past participle tæht) "to show, point out, declare, demonstrate," also "to give instruction, train, assign, direct; warn; persuade," from Proto-Germanic *taikijan "to show" (source also of Old High German zihan, German zeihen "to accuse," Gothic ga-teihan "to announce"), from PIE root *deik- "to show, point out." Related to Old English tacen, tacn "sign, mark" (see token). Related: Taught; teaching.

Lemonade Vendor (Edgar Kennedy), enraged: I'll teach you to kick me!
Chico: you don't have to teach me, I know how. [kicks him]

The usual sense of Old English tæcan was "show, declare, warn, persuade" (compare German zeigen "to show," from the same root); while the Old English word for "to teach, instruct, guide" was more commonly læran, source of modern learn and lore.