Atlantis
Atlantis is a lost island civilization of Earth mentioned and described in two dialogues of Plato, Timaeus and Critias. These two dialogs are the only sources we have for this myth. According to Plato, who cites Solon the Lawgiver as his source, Atlantis was a large island in the "Atlantic Sea" somewhere beyond the Pillars of Hercules. The Atlanteans originally were a virtuous race, but later erred from the path of virtue and attempted to conquer the entire Mediterranean world, getting involved in a war with Athens and Egypt. The gods punished Atlantis by destroying the island, which is said to have happened 9,000 years before Solon's visit in Egypt where he received the tale.
Most scholars now think that Plato simply made up the tale; but many (both serious academics and amateurs) have sought Atlantis in many different locations, some blatantly implausible, others reasonably conceivable. A popular image is that of a lost continent in the middle of the Atlantic Ocean, but geological evidence speaks against that, and it is not certain whether the "Atlantic Sea" of Plato's tale can be simply equated with what is now called the Atlantic Ocean. The most frequently discussed of the less implausible localizations equates Atlantis with the Minoan civilization and the fall of Atlantis with the eruption of the Santorini volcano; however, the Minoan civilization was obviously not "beyond the Pillar of Hercules", and the years elapsed after the catastrophe would have to be divided by 10 (perhaps a translation error?).
Jörg Rhiemeier speculates that in the Atlantis tale, the downfall of the Minoan civilization became confused with the story of another civilization, the British Elves. Atlantis would then have been Britain, and the "Atlantic Sea" the North Sea.
Atlantis has been the subject of many novelizations and media adaptations, such as the 2001 animated film Atlantis: The Lost Empire, which features a conlang. Another famous Atlantis adaptation is Númenor in The Silmarillion by J. R. R. Tolkien, which features another conlang.