  In this paper we study the class of so-called privileged words which have
been previously considered only a little. We develop the basic properties of
privileged words, which turn out to share similar properties with palindromes.
Privileged words are studied in relation to previously studied classes of
words, rich words, Sturmian words and episturmian words. A new characterization
of Sturmian words is given in terms of privileged complexity. The privileged
complexity of the Thue-Morse word is also briefly studied.
