While there may have been older games that have been lost to time and memory entirely, the oldest one we have evidence and rules for is The Royal Game of Ur, circa 2600-2400 BC or so. That date is an estimate based on a surviving board that is now held by the British Museum. The rules remained unknown for a long time until the 1980s, when professor Irving Finkel at the museum translated a slightly younger cuniform tablet and from there, was able to reconstruction the basic rules. Finkel himself is still around and has even made youtube videos about how the game is played. He's quite entertaining watch, in that slightly mad professor/possible-immortal-wizard sort of way.

Board games have a kind of taxonomy based on their various rule designs. This is touched upon in great detail in notable game historian David Parlett's History of Board Games. While this is not an exact science, it's generally agreed that the Game of Ur belongs to the "tables" game family. This is the same family as backgammon, in that in involves each player having multiple pieces which advance around a course via roll of the dice, with the strategy being which piece to move, and having the mechanic of bumping the opposing player's pieces off by landing on them. There are numerous evolutions of this concept, with Tabula during the Greek and Roman times, Nard in ancient Persia, numerous variations in the Middle Ages which are documented in the 13th century Spanish book Libro de Lose Juegos, and eventually Backgammon around about the 17th century.