The Edinburgh International Festival is the original and "official" festival. Initiated in 1947, the International Festival brings top class performers of classical music, theatre, opera and dance from around the world to perform, by invitation from the Festival Director only (information from wikipedia).
This year's highlights (for August 2010) include performances of the Gershwins' opera Porgy and Bess, the world premiere of the play Caledonia - the story of a small, poor country mistaking itself for a place that is both big and rich, the music of Korngold and Brahms performed by the Cleveland Orchestra (I have to give a shout out to my hometown!) and energetic and sensual dancing inspired by the paradise that is Brazil.