The Anglo-Saxon rune set was adapted early in the 6th century B.C.E. from a rune row known as the Frisian rune row. The Frisian runes were the result of a rapid change in the language in Frisia. With such a rapid change in the language more runes were eventually needed so the Elder Futhark was expanded by 4 symbols to bring the Frisian rune row to a total of twenty-eight rune staves. Later around the 7th century a twenty-ninth rune, Ear, was added to form the Anglo-Saxon rune set.
When the rune row was expanded a slight change was made to the order of the set. Ansuz, the fourth rune of the Elder Futhark, was replaced with a new rune, Os and Ansuz was renamed Aesc. While this may have been the only change to the shapes and names of some of the runes it was not the only change in rune order that we come across with this set (and its similar sets). In various manuscripts and on some carvings we see the runes in different orders. On a knife found in the Thames River in London we see the full rune row but in a different order. On the Thames River knife we still see that the fourth rune is Aesc, but the last eight runes are arranged differently leaving the rune Ear to be at the end of the rune order.
Most of the information for the order of the Anglo-Saxon and Frisian rune sets is known because of the Thames River knife, also known as the Thames scramasax, and the Vienna Codex. The Vienna Codex is an early 9th century Anglo-Saxon manuscript that does provide a complete version of the Anglo-Saxon rune row.