The Geometry of the Octonions

[2] Its contents combine both a survey of past work in this area, and much of its authors' own researches.

[4] Reviewer Danail Brezov notes with disappointment that Clifford algebras, although very relevant to this material, are not covered.

[3] The second part of the book uses the octonions and the other division algebras associated with it to provide concrete descriptions of the Lie groups of geometric symmetries.

[2][4] The third part applies the octonions in geometric constructions including the Hopf fibration and its generalizations, the Cayley plane, and the E8 lattice.

[2][3][4] It also includes material on octonionic number theory,[3][4] and concludes with a chapter on the Freudenthal magic square and related constructions.