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¡¡¡¡from the reviews of the 1st edition: "this book provides a comprehensive and detailed account of different topics in algorithmic 3-dimensional topology, culminating with the recognition procedure for haken manifolds and including the up-to-date results in computer enumeration of 3-manifolds. originating from lecture notes of various courses given by the author over a decade, the book is intended to combine the pedagogical approach of a graduate textbook (without exercises) with the completeness and reliability of a research monograph--- all the material, with few exceptions, is presented from the peculiar point of view of special polyhedra and special spines of 3-manifolds. this choice contributes to keep the level of the exposition really elementary. in conclusion, the reviewer subscribes to the quotation from the back cover: "the book fills a gap in the existing literature and will become a standard reference for algorithmic 3-dimensional topology both for graduate students and researchers".r. piergallini, zentralblattfilr mathematik 1048 (2004) for this 2nd edition, new results, new proofs, and commentaries for a better orientation of the reader have been added.