Per Sigurd Agrell's  Uþark Rune Theory

What is the Uthark?

Per Sigurd Agrell (Born 16 January 1881 in Värmland, Died 19 April 1937 in Lund) was a Swedish poet, translator, runologist, and professor of Slavic languages at Lund University. Professor Agrell was also the originator of the Uthark sequencing of the Fuþark rune-set: Sigurd demonstrated through his controversial and highly speculative theory that each rune has a numerical value. He called this the Uthark theory, since it is based upon a removal of the Féo rune from the first position in the Fuþark . The Féo rune is instead inserted as the last rune, and so all runes are shifted one step. 

There exist, however, some slightly different versions of the Fuþark , and Sigurd Agrell was not completely sure of which one to use for his theory. Sigurd Agrell explains in his book "Runornas Talmystik och dess antika förebild" (1927), the fact that the rune Dagaz comes before Othilla on the "Kylver Grave Slab" as well as in some Anglo-Saxon rune alphabets and is most probably a misunderstanding. By the 5th-century CE. Ehwaz and Pertho were becoming obsolete in the practical sense of writing, which meant that only the truly competent knew the original order of the runes. Ehwaz and Pertho are in an opposite order on the "Kylver Grave Slab", and so are Dagaz and Othilla, but on all bracteates (round pendants with the runes in a circular pattern) the order is different; and considering the fact that the "Kylver slab" is an exception in Scandinavia, Sigurd draws the conclusion that the rune sequencing order on the pendants are in fact the true accurate order; therefore, Othilla precedes Dagaz... In 1925, Sigurd claimed that the rune alphabet was modelled on the more-or-less reconstructed magical alphabet of numbers and symbols employed by the ancient mystery-cult of Mithra; this cult practiced bull-worshipping, and therefore, according to Agrell, the Uruz-rune associated with the mythological bull occupied the first place in his alphabet. According to Agrell, the runes were originally used solely for magical purposes, and when the runes started to be used for mundane writing, the last F-rune was moved to the beginning of the alphabet in order to hide the magic origins and use of this theoretical rune alphabet. Agrell's Uthark-theory is controversial, and remains yet to be scientifically proved.

Agrell's numerology theory and how Odin's Galder song is created is described in the book Sigurd Agrell Lapptrummor och Runmagi: Tvenne kapitel ur Trolldoms Vesendets Historia, C. W. K. Gleeryps Forlag Lund 1934, Sweden (Republished by Psychick Release, Stockholm, 1991)

Spiegelrunen or mirror-runes are also said to belong to the enigmatic category. Mirror-runes are those which are in fact double-sided versions of one rune. Sometimes they consist of one hasta with symmetrical twigs, pockets or loops on either side, in such a way that the rune gives the impression of being mirrored [Fig 1]. Others show the same shape on the upper and lower part [Fig 2], or same shape to the right and left [Fig 3]. These runes should be read as one rune, not as two. These peculiar rune shapes are sometimes referred to as ‘ornamental runes' 

—Ref: (Pieper 1987; Looijenga 1995a)

Modern Ideas About Runes

According to some academia, there is no current scholarly consensus about exactly when or where the runic alphabet originated from; although there is considerable evidence that runes may be an evolution of the Danube Culture semiotic scripts. The likelihood of establishing conclusive proof the runes derived from other writing systems is a possibility, but the daunting task lies in positively establishing when & who first used and sounded these symbols. Nevertheless, it is not clear that runic writing arose from the interactions the Germanic-speaking peoples had with the cultures of the Southeastern Europe, where the ideas of alphabetic writing came about; and that some of the runic characters (though not ordered like the alphabet) may demonstrate the influence of Etruscan writing. However, recent discoveries of much older Runes in use in Northern Europe have definitively contradicted the ideas that Runes were adapted from the Roman alphabet. Alternative theories speculate that Runes were derived from the Danube Culture script--a writing system in use thousands-of-years BCE in Southeast Europe

The lack of archaeological specimens of rune-sets tends to contradict the notion that fuÞark runes were carried around in convenient rune pouches. This idea is likely a modern one whose consensus stemmed from the early 70’s when the New Age renaissance surrounding all-things mystical or magical was in popular demand. Many accept it as true that, historically, runes were never carried in pouches; but rather, runes were held within the minds of those who wielded them, and they were created (cut) on each occasion in to wood (not stones), ‘blooded’ by the runemaster, and then destroyed by fire after their use in ritual.

Runes: Magicality & Literality

Þat kann ek it fiórða I know the fourth

ef mér fyrðar bera if men fasten

bönd at bóglimum locks on my limbs

svá ek gel I sing a spell

at ek ganga má— so I may step free —

sprettr mér af fótum fjöturr the fetters snap off my feet

en af höndum hapt the hasp off my hands!

—Hávamál stanza 149

Bede substitutes a superstitious interpretation of the “loosening bonds” being caused by written spells with the central Christian rite of the recitation of the mass, replacing older cultural interpretations and asking the reader to recognize the miraculous from a Christian perspective. It is not even clear whether Bede is referring to runes in this episode, or to general superstitions about the act of writing and the power of words; and his reluctance to elaborate on the fable may well constitute an ‘act of literary suppression’ as Seth Lerer suggests (1991: 39). The Old English translation, however, seeks to make some sense of this allusion to letters-which-are-loosening through the concept of written characters and the ‘releasing rune’:

Ond hine ascode hwæðer he ða alysendlecan rune cuðe, and þa stafasmid him awritene hæfde, be swylcum men leas spel secgað and spreocað, þæt hine mon forþon gebindan ne meahte.

“And he asked him whether he knew the releasing rune, and had with him the letters written out, such as men tell idle tales of and speak about, so that, for this reason, he could not be bound.”

—(Old English Version of Bede’s Ecclesiastical History 4/22: 328)

There is considerable uncertainty as to the earliest purpose of the runes, whether they were originally used as characters for writing, or as the name suggests: as mystical signs—bearers of potent magic. But, since the power and force of the spoken word easily pass into the symbol for which it stands, it is not improbable that the latter meaning is secondary, the spell becoming materialized through the graven symbol, and—even in this form—retaining all its original power for good or evil. It is well-established that the earliest Germanic literature is abundant in proofs of the magic nature of runes; from the Edda poems down to the latest folksongs of the present day, there is continuous evidence of their mystic influence over mankind. Runes could raise the dead from their graves; they could preserve life or take it; they could heal the sick or bring on lingering disease; they could call forth the soft rain or the violent hailstorm; they could break chains and shackles or bind more closely than bonds or fetters; they could make the warrior invincible and cause his sword to inflict none but mortal wounds; they could produce frenzy and madness or defend from the deceit of a false friend. Their very origin was understood to be divine, since Odin is described in the Edda as sacrificing himself in order to learn their use and hidden wisdom.

Ref: The Cambridge History of English and American Literature in 18 Volumes (1907–21). Volume I. From the Beginnings to the Cycles of Romance. Runes in Scandinavian and Old English Literature.