The Ancient Language, in the world of Eragon. Is a language origonating from the elves in the Inheritance Trilogy.
Origins
In myth the Ancient Language came to Alalgaesia along with the elves. Who landed on the western coasts before any recorded time. The language was used by Shades, Dragon Riders, and other magical creatures. According to Brom in the first book in the Inheritance Trilogy a word for the ancient language "means" the world, so if someone said "brisingr" a fire would spark in front of them. Brom also quoted that you cannot lie in the Ancient Language, which comes to sense later in the book.
Riders and Their Relations with Magic
The Dragon Riders use the ancient language to use "magic" but unlike most beings in Inheritance they use the magic from their dragons. The magic courses through them and they are able to do as they wish as long as it is in their range (some spells can severely weaken or kill unexperienced riders). In Eldest, Eragon stores his magical energy in diamonds in his sheath. As well as Saphira, who in Eragon turns Brom's sandstone tomb to diamond so Brom's body would never weather. Later in the book Saphira states that she has no control over her abilities.