We consider several basic notions of combinatorics on words, either directly related to applied algorithmic problems, or of theoretical interest.

Is there a word on a finite alphabet which does not contain two consecutive equal subwords? How can we estimate the number of words of a given length avoiding factors of a given form? How many factors of a given length can a word have? And what about words appearing in its arithmetic progressions? What theory arises from words coding discretized straight lines?