  Normed division rings are reviewed in the more general framework of
composition algebras that include the split (indefinite metric) case. The
Jordan - von Neumann - Wigner classification of finite dimensional Jordan
algebras is outlined with special attention to the 27 dimensional exceptional
Jordan algebra J. The automorphism group F_4 of J and its maximal Borel - de
Siebenthal subgroups are studied in detail and applied to the classification of
fundamental fermions and gauge bosons. Their intersection in F_4 is
demonstrated to coincide with the gauge group of the Standard Model of particle
physics. The first generation's fundamental fermions form a basis of primitive
idempotents in the euclidean extension of the Jordan subalgebra JSpin_9 of J.
