Octonion Algebras Over Number Fields Is there any textbook or paper about Arithmetic of Octonion Algebras or Octonion Algebras constructed over number fields?
I know J. Voight book and K. Martin notes about quaternion algebras but I was thinking about a generalization using Octonions.
More than that: Is it possible to define Orders and Maximal Orders over an octonion algebra? Or these concepts just make sense over associative algebras?
 A: I actually have a mostly written chapter on Octonions in my personal version of my quaternion algebra notes, which I might finish up and post if I ever teach that course or start thinking about these things again.  
Anyway, there are far fewer octonion algebras than quaternion algebras, as mentioned in @pregunton's comment.  Basically at a finite place you only have a local split octonion algebra and over a real place you can have the split or non-split one, leading to $2^r$ octonion algebras over a number field with $r$ real places.  This is in the beginning of Springer and Veldkamp's book.  You could also check some books on composition algebras.
You also have a notion of orders and maximal orders.  For facts about the usual octonions $\mathbb O$ over $\mathbb Q$, see Conway and Sloane's book and Baez's Bulletin article.  The former talks about various orders and factorization problems, the latter of which have since been studied in a few "meta-commutation" articles.  van der Blij and Springer (1959) show all maximal orders of $\mathbb O$ (and as I recall any definite octonion algebra) are isomorphic.  Susanna Epp in the 70's also studied orders in octonion algebras (look for the term "Cayley algebra").
