We know from a section of the Hávamál (Sayings of the High One) from the Elder/Poetic Edda that Odin gained the Runes or knowledge of them via an act of self sacrifice. This section of the Havamal is called the Rúnatal:
"I know that I hung on a windy treenine long nights,
wounded with a spear, dedicated to Odin,
myself to myself,
on that tree of which no man knows
from where its roots run.
No bread did they give me nor a drink from a horn,
downwards I peered;
I took up the runes, screaming I took them,
then I fell back from there. (verses 138-139, Larrington translation)
A more poetic yet older translation by Benjamin Thorpe translates the Old Norse as:
"I know that I hung, on a wind-rocked tree, nine whole nights, with a spear wounded, and to Odin offered, myself to myself; on that tree, of which no one knows from what root it springs.
"Bread no one gave me, nor a horn of drink, downward I peered, to runes applied myself, wailing learnt them, then fell down thence." (verses 140-141)
As I am sure that my readers will agree the Thorpe translation being older is more poetic but it needs to be borne in mind that newer translations tend to be more accurate. Without studying the relevant passages in the original Old Norse I cannot at this stage comment on whether the version of this passage by Carolyne Larrington is more accurate. The translations though are essentially the same apart from one important point. Thorpe states Odin "applied" Himself to the Runes and "wailing learnt them". By contrast Larrington does not say that Odin learned the Runes only that He "took them".
The translation of the second verse by Hollander:
"Neither horn they upheld nor handed me bread; I looked below me- aloud I cried- caught up the runes, caught them up wailing, thence to the ground fell again."
Again, no reference to learning the Runes. The translation by Bray:
"None refreshed me ever with food or drink, I peered right down in the deep; crying aloud I lifted the Runes then back I fell from thence."
The translation by Bellows:
"None made me happy with loaf or horn, And there below I looked; I took up the runes, shrieking I took them, And forthwith back I fell."
The translation by Terry:
"They brought me no bread, no horn to drink from, I gazed towards the ground. Crying aloud, I caught up runes; finally I fell."
The translation by Auden:
"They gave me no bread, They gave me no mead, I looked down; with a loud cry I took up runes; from that tree I fell."
And finally the translation by Chisholm:
They dealt me no bread, nor drinking horn.
I looked down, I drew up the runes,
screaming I took them up,
and fell back from there.
Out of the 8 translations the one by Thorpe is the only one which makes reference to 'learning' the Runes but that fact of course does not in itself make Thorpe's translation of the verse incorrect. When translating from ancient languages into a modern one the translator often does not know the exact meaning or the nuance of the word he is translating and just as in modern English a word with identical or similar spelling can have a radically different meaning. Despite Thorpe being 'out on a limb' with this verse it is his translation which I feel captures the essence of it best! It is quite clear that Odin after having gained the Runes would by necessity have had to learn and interpret them. The Runes did not originate with Odin but He discovered or more likely rediscovered them and then gave this knowledge to man for immediately after the Rúnatal we have the Ljóðatal which goes on to list 18 Rune charms or songs.
Readers of this article are advised to also read Odin on the World Tree