Wisdom in Norse mythology is never given. It is bought, and the currency is always a piece of the body.
Mímir is the counterparty in the two largest transactions. Odin leaves an eye in his well to drink from it. Then, later, Mímir loses his head — and Odin keeps that too, and consults it. A one-eyed god carrying a talking severed head is not a dignified image, and the sources present it without embarrassment.
The well
Völuspá stanza 28 is the earliest statement and it is compressed to the point of riddling: the seeress says she knows where Óðinn's eye is hidden, in the famous well of Mímir; Mímir drinks mead every morning from Valföðr's pledge.
That is all. The eye is a veð, a pledge — a legal deposit against a debt, not a payment. Snorri expands it in Gylfaginning: the well lies under the root of Yggdrasil that reaches toward the frost-giants, wisdom and understanding are hidden in it, its owner is called Mímir and he is full of knowledge because he drinks from it with the Gjallarhorn, and Alföðr came and asked for one drink and did not get it until he had given his eye in pledge.
The economics are precise and slightly bleak. Odin does not buy the well. He buys one drink, and the deposit is permanent.
The head
Ynglinga saga tells the other half, in Snorri's euhemerised register. At the settlement of the Æsir–Vanir war, hostages are exchanged: the Vanir send Njörðr and Freyr, and the Æsir send Hœnir — tall, handsome, and, as the Vanir gradually work out, incapable of making a decision without Mímir standing next to him telling him what to say. Feeling cheated, the Vanir cut off Mímir's head and send it back.
Odin takes the head, smears it with herbs so it will not rot, and sings charms over it, and thereafter it speaks with him and tells him hidden things.
Sigrdrífumál refers to runes cut on the head of Mím and read aloud, and Völuspá has Odin speak with Mím's head at the very last moment before Ragnarök begins — after Heimdall's horn sounds and before the fighting. It is his final consultation, and the poem does not report the answer.
Is he a giant, a god, a hostage, or the water?
The sources will not agree.
- Völuspá calls the well Mímisbrunnr and treats Mímir as its owner and drinker.
- Gylfaginning has him as a proprietor of wisdom under the tree, not obviously counted among the Æsir.
- Ynglinga saga has him as one of the Æsir, valuable enough to send as a hostage.
- Skaldic kennings call Yggdrasil Mímameiðr, Mímir's tree, and Fjölsvinnsmál uses that name for a tree with properties Yggdrasil does not clearly have elsewhere.
- The survivors of Ragnarök in Vafþrúðnismál hide in Hoddmímis holt, Hoard-Mímir's wood, and repopulate the earth — which places a Mímir-name at the end of the world as a place of shelter.
There is also a form Mímr alongside Mímir, and the byname Sökkmímir, applied to a giant Odin kills. The likeliest reading is that "Mímir" designates a category — a memory-power associated with a water source and a tree — rather than a single character with a biography, and that the different texts each grabbed a different piece of it. The name is usually connected to a root for memory, cognate with Latin memor.
The Irish and English parallels
Wells of wisdom under trees are not a Norse peculiarity. Irish tradition has Connla's Well and the Well of Segais, with hazels dropping nuts into the water and salmon eating them — knowledge acquired by ingestion from a spring under a tree, in a neighbouring culture the Norse were in constant contact with. Whether that indicates borrowing, common inheritance, or the independent obviousness of the image is unsettled; see the Norse and Celtic otherworlds.
Mimir in the modern imagination
God of War (2018) gave Mimir a leading role as a talking severed head with a Scottish accent, chained to a tree until Kratos frees him and carries him on his belt as a narrator. It is by a wide margin the most prominent Mimir has ever been, and the head-as-companion premise is genuinely from the sources — the Celtic-flavoured backstory, the wit and the name "Puck" are not. Marvel's Odin has no Mimir at all.
Modern Scandinavian usage keeps the word: Swedish and Norwegian firms and schools take the name for its associations with knowledge, and mimre survives dialectally around ideas of remembering. For the wider question of how much of this pantheon is Snorri's arrangement rather than inherited belief, see the Norse overview, and for what Odin paid elsewhere, his own entry and the well myth.
Is the eye in the well, or is the eye the drinking vessel?
Both readings exist and the Old Norse is genuinely ambiguous. Völuspá says Mímir drinks from Valföðrs veði — "the pledge of the Father of the Slain" — and if that pledge is the eye, then Mímir is drinking his morning mead out of Odin's eye socket, or out of the eye as a cup. Snorri instead has Mímir drink from Gjallarhorn, which tidies the image considerably and may be exactly why he did it. Some editors read the eye as simply deposited in the water. The grisly version has the better claim to being what the poet meant.
Why would the Vanir behead a hostage rather than return him?
Hostage exchange in early medieval northern Europe was a mechanism for guaranteeing a treaty, and mistreating a hostage was how a party signalled that it considered the treaty broken or fraudulently obtained. The Vanir's complaint is specifically that they were given a defective exchange — Hœnir looked like a chief and could not function as one. Returning the head is a message about the quality of goods received, expressed in the most legible form available. That the Æsir respond by putting the head to work is entirely in character.