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This is the first volume of a systematic two-volume presentation of the various areas of research on structural complexity. The theory of algorithmic complexity, a part of the mathematical theory of computation, can be approached from several points of view, one of which is structural. The text has been aimed at undergraduate students who have taken a first course in formal language theory. It presents the basic concepts of structural complexity, thus providing the background necessary for the understanding of complexity theory. This corrected edition has been extended by an appendix with recent results on nondeterministic space classes and updated with regard to the bibliographical remarks and the references.