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These proceedings contain a collection of papers on Combinatorial Dynamics, from the lectures that took place during the international symposium, Thirty Years after Sharkovskiĭ''s Theorem: New Perspectives, which was held at La Manga del Mar Menor, Murcia, Spain, from June 13 to June 18, 1994.Since Professor A N Sharkovskiĭ''s landmark paper on the coexistence of periods for interval maps, several lines of research have been developed, opening applications of models to help understand a number of phenomena from a wide variety of fields, such as biology, economics, physics, etc. The meeting served to summarize the progress made since Professor Sharkovskiĭ''s discovery, and to explore new directions.