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This Special Issue of RAIRO, Theoretical Informatics and Applications is devoted to full versions of selected papers from the workshop Word Avoidability, Complexity and Morphisms which took place in Turku (Finland) on July 2004, as a satellite event of the conference ICALP'2004. The topics of this one day workshop concern particular aspects of Combinatorics on Words: string pattern avoidability, complexities of finite or infinite words, and free monoids morphims. The scientific program of the worshop consisted of two invited lectures given by A.E. Frid and J. Shallit as well as presentations of 8 contributed papers selected by the Program Committee from a total of 12 submissions. The Program Committee consisted of : A. Carpi (Perugia), J. Cassaigne (Marseille), J. Currie (Winnipeg), I. Petre (Turku), G. Richomme (Amiens), A. M. Shur (Ekaterinburg), and P. Séébold (Montpellier). This special issue contains the full text of five of the papers presented at the workshop. All of them were normally refereed and revised. I would like to thank everybody who contributed to the workshop and this issue including invited speakers, members of the program Committee, ICALP'2004's organization, authors and all referees of papers submitted to the worshop and this special issue. I am indebtful to J. Kärhumaki and J. Berstel for thinking of me to organize this workshop. Special thanks to P. Séébold for all his advices. Finally I am grateful to C. Choffrut, the editor-chief of the RAIRO-TIA for accepting to publish this special issue.