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The subject of this book is the action of permutation groups on sets associated with combinatorial structures. Each chapter deals with a particular structure: groups, geometries, designs, graphs and maps respectively. A unifying theme for the first four chapters is the construction of finite simple groups. In the fifth chapter, a theory of maps on orientable surfaces is developed within a combinatorial framework. This simplifies and extends the existing literature in the field. The book is designed both as a course text and as a reference book for advanced undergraduate and graduate students. A feature is the set of carefully constructed projects, intended to give the reader a deeper understanding of the subject.

Combinatorial analysis. --- Permutation groups. --- Ordered algebraic structures --- Discrete mathematics --- 512.54 --- Combinatorial analysis --- Permutation groups --- Substitution groups --- Group theory --- Combinatorics --- Algebra --- Mathematical analysis --- 512.54 Groups. Group theory --- Groups. Group theory --- Groupes de permutations --- Analyse combinatoire