  This paper is devoted to survey composition algebras and some of their
applications.
  After overviewing the classical algebras of quaternions and octonions, both
unital composition algebras (or Hurwitz algebras) and symmetric composition
algebras will be dealt with. Their main properties, as well as their
classifications, will be reviewed. Algebraic triality, through the use of
symmetric composition algebras, will be considered too.
