Aelic. The common tongue in the Western Isles, spoken by nearly all humans and halflings there, as well as most others on Aeldynn. Not nearly as common elsewhere, but still something of a lingua franca. Aelic uses the Matican alphabet.
Kwnseviki. Historically the dominant language on the Isle of Vess (formerly Kwnsevik), Kwnseviki is now primarily a language of the underclass on the Isle, and a language of refugees and exiles elsewhere. Kwnseviki uses the Matican alphabet. (Koon-suh-vee-kee)
Vamenlugha. Known to outsiders as Halfling, Vamenlugha (literally “the family’s language”) is a creole language formed over centuries from Aelic and a now-lost halfling language. Halflings rarely teach it to outsiders. Vamenlugha uses the Matican alphabet, with a few modifications.
Vessic. Once a regional dialect, Vessic has recently become a very prominent language. It is the official language of the Vessic Empire, and is rapidly becoming widely spoken across the Isle of Vess. Vessic uses the Matican alphabet.
Old Matican. Old Matican (or Ancient Matican) is a language used by the ancient inhabitants of the Western Isles. Before the Conflagration, the Maticans were very powerful--consequently, most languages on the Western Isles are descended from Old Matican, and use variants of the Old Matican alphabet. However, the modern Matican alphabet is somewhat different from Old Matican--a few letters have been lost, and many have changed shape somewhat.
Ordjarnskr. Originally spoken by giants and giant-kin on the Northern Isles, Ordjarniskr has become something of a lingua franca in the Northern Isles. Elsewhere, people usually refer to it by the exonym “Ordari,” from the Asari name for the giants. While Ordjarniskr has various regional dialects, most are fairly closely related. Ordjarniskr shares a common ancestor with the Dwarven languages, and it is written using a related abjad script.
Draconic. Called Draconic by outsiders, the dragon-tongues consist of three (or, arguably, countless) related languages with very distinct origins. All use a similar, cuneiform-like script.
High Draconic. High Draconic is a magical language that all dragons hatch with a complete knowledge of--both the spoken and written forms. High Draconic has very complex grammar and an expansive vocabulary, making it very difficult to learn for those who do not innately know it--so, all non-dragons. Because High Draconic is an innate language--known by all dragons at birth--it is supernaturally unchanging, and never subject to linguistic drift.
Low Draconic. Low Draconic is any of the countless ways in which the kobolds who serve dragons adapt High Draconic into a language that is actually usable in a straightforward manner by non-dragons. While Low Draconic is arguably many thousands of different languages, kobolds are generally fairly predictable in how they derive their tongues from the universal and immutable High Draconic, so most forms of Low Draconic are relatively similar. Low Draconic is rarely written (outside of very simple one-word warnings and signals), because most kobolds are almost illiterate. Most literate kobolds also know High Draconic, and so prefer to use it instead--High Draconic is seen as a more elegant and fitting tongue with which to write magic or history.
Middle Draconic. Middle Draconic is spoken by the Dragonborn of the Northern Isles. It descends from a specific dialect of Low Draconic, with a number of influences from High Draconic, Ordjarniskr, and the Dwarven languages.
Dwarven Languages. The Dwarven people were fractured during the Conflagration: some remain in the Dwarven heartland in the Northern Isles, some reside in the Western Isles, and some fled beneath the ground to the Underdark. Their langauges are correspondingly fractured--although they are, generally, mutually intelligible. All Dwarven languages are related to Ordjarnskr, and use the same, abjad-like script.
Veteracht. Spoken by most dwarves and gnomes of Aeldynn. Because it literally translates to “traitor-tongue,”--a remnant of an almost-forgotten grudge--many who speak it use the similar-sounding name “Vestenracht,” or “west-tongue.”
Altenracht. Literally the “old tongue,” spoken by the dwarves and gnomes of the Northern Isles. Out of all Dwarven languages, Altenracht the most resemblance to Ordari, with which it is almost mutually intelligible.
Adamanteracht. Literally “deep-tongue,” “strong-tongue,” or “adamantine-tongue” (these are all roughly synonymous), Adamanteracht is spoken by the deep dwarves and gnomes of the underdark and the Shadowfel. Consequently, it has incorporated a number of loanwords from Aluthri. It is rarely heard on the surface.
Elvish Languages. There are five main Elvish tongues, all (allegedly) descended from the legendary Aprimalfi. Each dialect is functionally a separate language, though they do have similarities, and all use the flowery, circular Elvish script.
Aelfwyri. Spoken by the high elves, Aelfwyri is an incredibly complex and idiosyncratic language. It takes years of study to learn the grammar and vocabulary, but even that isn't sufficient--the Aelfwyr speak in endless references to millenia-old poems, plays, novels, and epics. To speak Aelfwyri fluently is to have a near-comprehensive knowledge of thousands of years of high elf literature--a task impossible for all except the immortal Aelfwyr.
Asari. The "standard" Elvish language in Aelfwyr, Asari is spoken by wood elves. There are some differences regionally, but the Asari spoken in the Western Isles is still relatively close to the language spoken in Aien Asari, the ancient forest homeland of the Asar in the Northern Isles.
Aluthri. Spoken by the dark elves beneath the world. While the dark elves call themself the Aluth, people on the surface tend to call them Drow--a name that they consider a slur. Aluthri is mutually intelligible with Kontari.
Kontari. Spoken by the sand elves of the wide deserts in the Southern Isles, Kontari is lilting and oddly slow. Kontari is mutually intelligible with Aluthri.
The Grey Tongue. All goblinoids can speak the Grey Tongue once they reach a few years of age. It is innate, unchanging, and clearly supernatural. Goblinoid priests will tell you that Maglubiyet, the Conquering God, wrote the language into their blood when he turned it grey and claimed the goblins, hobgoblins, and bugbears as his own. The supernatural and innate language of the Grey Tongue is considered by many to be the single strongest piece of evidence for the existence of the Blood Gods.
Spirit Languages. On each plane, there exist spirits, more-or-less eternal beings who are the physical and metaphysical embodiments of the plane. Druids and their ilk communicate with these spirits--whether knowingly or not--by speaking their languages, which are innate and eternal (similar to Draconic). While some of these languages are secret--and the rest very uncommonly spoken--none of them are particularly difficult to learn. In fact, they are all remarkably regular, straightforward, and symmetrical in a way that no mortal language is. Because these languages seem to be innate to their planes, scholars often look at them to gain insight into the fabric of the multiverse--typically with limited success.
Druidic. Spoken by spirits and druids on the material plane. Druidic is a secret language.
Sylvan. Spoken by spirits and druids in the Feywild. It is unusual amongst spirit languages in that variants of it are very commonly spoken by others in the Feywild. Feywild spirits are active and social enough that Sylvan has become something of a lingua franca amongst the people of the Feywild--thus, unlike most other spirit languages, Sylvan is not a secret language.
Fetchen. Spoken by spirits and druids in the Shadowfel. Fetchen is a secret language.
Abyssal. A language of the planes, spoken by outsider spirits who cause chaos and destruction--otherwise known as fiends, demons, demodands, or Tanar'ri.
Celestial. A language of the planes, spoken by a wide variety of (usually) broadly benevolent outsider spirits who seek to ameliorate suffering or impose some kind of justice upon the universe.
Infernal. A language of the planes, spoken by outsider spirits whose interaction with nonspirits center around sowing fear, wrath, or emptiness--devils, fiends, yugoloths, or Baatezu.