Týr's name is the oldest thing about him, and it is the reason his myths do not fit him.
Linguistically, Týr descends from Proto-Germanic *Tīwaz, which continues Proto-Indo-European *dyēus — the same root that produced Greek Zeus, Latin Iuppiter (from dyeu-pater) and Sanskrit Dyaus Pitṛ. It is not merely related to the word for god; in Old Norse týr remains a common noun meaning "a god," and appears in the plural tívar for gods generally, and inside Odin's own bynames — Hangatýr, Farmatýr, Sigtýr. The word that once named the sky-father had become, by the Viking Age, a generic label that other gods wore as a suffix.
Something happened to this deity between the Bronze Age and the Eddas, and nobody knows what.
The one myth that is entirely his
Gylfaginning tells it in a few hundred words. The gods raise Loki's wolf-son Fenrir among themselves, and only Týr is brave enough to feed him. As the wolf grows to a size that alarms everyone, they attempt to bind him twice with ordinary fetters, presenting each as a test of strength; he breaks both and gains a reputation from it. The third fetter, Gleipnir, is a silk-thin ribbon made by dwarfs from impossible materials, and Fenrir — no fool, and by now suspicious — agrees to be bound by it only if one of them will place a hand in his mouth as a pledge of good faith.
The gods look at one another. Týr puts in his right hand.
The binding holds. Fenrir bites the hand off at the wrist. Snorri notes, drily, that the gods laughed, all except Týr.
The god of oaths gives a pledge he knows is worthless, on behalf of a group that wants the wolf bound and will not pay the price themselves. He is maimed for it and permanently loses his sword-hand, which for a god of single combat is not a decorative injury. This is the clearest instance in Norse myth of a deity accepting a real, irreversible personal cost for a communal good, and it is told without a word of moralising.
Mars Thingsus on Hadrian's Wall
Around 222 CE, Frisian soldiers stationed at Vercovicium — the fort now called Housesteads — set up an altar inscribed to Mars Thingsus and two goddesses called the Alaisiagae, on behalf of the emperor's welfare. The altar survives. Thingsus is the Germanic þing, the legal assembly.
That is a Roman-period inscription, in Britain, made by continental Germanic speakers, identifying their war-god with Mars and attaching him explicitly to the law-court. The Roman interpretatio that gives us the weekday names does the same: dies Martis became Old English Tīwesdæg, modern Tuesday, and Old Norse týsdagr, Swedish and Danish tisdag. Germanic speakers looking at Mars saw Týr.
So the association of this god with law and with assembly is not an Icelandic literary invention. It is attested in stone, in Britain, a thousand years before Snorri.
The rune, and the runic evidence
The ᛏ rune is named Tīwaz / Týr — one of only a handful of runes named after a deity. Sigrdrífumál instructs that victory-runes should be cut on the sword hilt and the name of Týr spoken twice. Migration-period and Viking-age weapons do carry ᛏ repeated in sequence, which is one of the rare cases where a poetic instruction and the archaeological record line up neatly. The rune shape — an upward arrow — is why Týr's mark has been adopted by everything from ski brands to political movements; see symbol traditions for how far that adoption has travelled from anything Norse.
Whose son is he?
Snorri makes Týr a son of Odin. The Eddic poem Hymiskviða has Týr propose fetching a brewing-cauldron from the giant Hymir, whom he calls his father, and describes visiting a hall with a nine-hundred-headed grandmother and a gold-bright mother who brings him ale. There is no way to reconcile the two: either Snorri assimilated an older independent god into Odin's family, as he does elsewhere, or Hymiskviða is using "father" loosely, which the language does not really support.
The family tree marks both parentages rather than choosing, and the disagreement is the single best small illustration of how the Norse pantheon was assembled — the systematiser tidying a figure who did not originally belong to the household he is being filed under.
The rest is fragments
He is present at Ægir's feast in Lokasenna, where he defends Freyr, and Loki's rejoinder is that Týr cannot make things equal between people because he lost a hand — and that Loki fathered a son on Týr's wife, a wife who is mentioned nowhere else and is never named. He appears in kennings as "the one-handed god" and "the wolf's leavings." At Ragnarök he fights Garmr, the hound of Hel, and each kills the other; Snorri says so, though Völuspá leaves it implicit.
That is close to the whole surviving corpus. For a god whose name is the oldest divine name in the language, whose rune is carved on weapons, whose day is in every Germanic calendar, and who appears on a Roman altar as the god of the assembly, the literary remains are almost nothing. Something removed him from the centre and the sources record only the result.
An arrow rune with an unhappy modern politics
Týr's modern presence is oddly split. He is a minor character in Marvel's films and an imprisoned pacifist in God of War Ragnarök — a striking reinvention, since it makes the war-god the one who refuses to fight, and there is no source basis for it at all. Meanwhile his rune has an unhappy political afterlife that has nothing to do with the medieval evidence and everything to do with 1930s Germany.
The version worth keeping is the one in Gylfaginning: a god who understands what an oath is well enough to know exactly what he is doing when he breaks one, and who does not complain afterwards. For what the wolf he bound goes on to do, see Ragnarök and the Norse tradition overview.
Was Týr ever the chief god before Odin?
It is a widespread claim and it rests entirely on etymology. The name descends from the Indo-European sky-father, so the argument runs that Týr held the top position and was displaced by Odin during the Migration Period. The evidence for the displacement itself is nil: there is no text or inscription showing Týr in charge of anything, and Tacitus in the first century already reports the Germanic peoples worshipping a Mercury-figure — Odin's equivalent — above all others. What we can say is that the name is ancient and the figure it now attaches to is not the one that name originally described.
Is the god Týr the same as the god in the Old English rune poem?
The Old English poem's ᛏ stanza describes Tīr as a certain sign that keeps faith well with nobles, always on its course above the mists of night — which sounds much more like a star or the polestar than a god. Whether the poet meant the deity, deliberately disguised the deity for a Christian readership, or genuinely thought the rune was named after a navigational fixed point is unresolved, and the ambiguity may be intentional on his part.