Brithenig is an invented language, or constructed language ("conlang"). It was created as a hobby in 1996 by Andrew Smith from New Zealand, who also invented the alternate history of Ill Bethisad to "explain" it.
Brithenig was invented neither to become used in the real world, like Esperanto, nor does it serve to provide detail to a work of fiction, like J.R.R. Tolkien's Elvish tongues, or Klingon from the Star Trek scenarios. Rather, Brithenig started as a thought experiment to create a Romance language that might have evolved if Latin had displaced Old Celtic as the spoken language of the people in Great Britain.
The result is a sister language to French, Spanish and Italian, albeit a test-tube child, which differs from them by having sound-changes similar to those that affected the Welsh language, and words that are borrowed from Old Celtic and from English throughout its pseudo-history.
Brithenig is respected among the conlang community, being the best-known example of the altlang genre. It is the first known conlang to extrapolate a real Terran language through an alternate evolution, and as such can be considered the grandfather of the genre.