On the Role of Division, Jordan and Related Algebras in Particle Physics

Part 1 Quaternions: algebraic structures Jordan formulation, H-Hilbert spaces and groups vector products, parallelisms and quaternionic manifolds quaternionic function theory arithmetics of quaternions selected physical applications historical notes. Part 2 Octonions: algebraic structures octonionic Hilbert spaces, exceptional groups and algebras vector products, parallelism on S7 and octonionic manifolds octonionic function theory arithmetics of octonions some physical applications historical notes. Part 3 Division Jordan algebras and extended objects: Dyson's 3-fold way - time reversal and Berry phases essential Hopf fibrations and D is greater than or equal to 3 anyonic phenomena the super-Poincare group and super extended objects.