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The second edition offers an in-depth introduction to the theory of classification, enumeration, construction, and generation of finite unlabeled structures in mathematics and the sciences. It highlights advancements since the first edition, notably the construction of first designs with moderate parameters. Key methodologies discussed include the use of automorphism groups and Kramer-Mesner matrices, alongside an improved LLL-algorithm for solving systems of linear equations. This edition also features new sections detailing significant contributions from various researchers in the field.