CAI 2009 was the Third International Conference on Algebraic Informatics. It was intended to cover the topics of algebraic semantics on graphs and trees, formalpowerseries, syntacticobjects, algebraicpictureprocessing, ?nite and- ?nite computations, acceptors and transducers for strings, trees, graphs, arrays, etc., decision problems, algebraic characterization of logical theories, process algebra, algebraic algorithms, algebraic coding theory, algebraicaspects of cr- tography. CAI 2009 was dedicated to Werner Kuich on the occasion of his retirement. ItwasheldinThessaloniki, Greece, duringMay19-22,2009andorganizedunder the auspices of the Department of Mathematics of the Aristotle University of Thessaloniki. The opening lecture was given by Werner Kuich, the tutorials by Alessandra Cherubini and Wan Fokkink, and the other four invited lectures by Bruno Courcelle, Dietrich Kuske, Detlef Plump, and Franz Winkler. This volume contains 2 papers from the tutorials, 5 papers of the invited lectures, and 16 contributed papers. We received 25 submissions, the contributors being from 14 and countries, and the Program Committee selected 16 papers. WearegratefultothemembersoftheProgramCommitteefortheevaluation of the submissions and the numerous referees who assisted in this work. We shouldliketo thankallthecontributorsofCAI2009andespeciallythehonorary guest Werner Kuich and the invited speakerswho kindly accepted our invitation to present their important work. Special thanks are due to Alfred Hofmann the Editorial Director of LNCS, who gave us the opportunity to publish the proceedingsofourconferenceintheLNCSseries, aswellastoAnnaKramerfrom Springer for the excellent cooperation. We are also grateful to the members of the OrganizingCommittee and a groupof graduatestudents who helped us with several organizing jobs.