  We investigate Abelian primitive words, which are words that are not Abelian
powers. We show that unlike classical primitive words, the set of Abelian
primitive words is not context-free. We can determine whether a word is Abelian
primitive in linear time. Also different from classical primitive words, we
find that a word may have more than one Abelian root. We also consider
enumeration problems and the relation to the theory of codes.
