The book "The Symmetric Group: Representations, Combinatorial Algorithms, and Symmetric Functions" is a comprehensive text on the symmetric group, covering representations, combinatorial algorithms, and symmetric functions. It is part of the Graduate Texts in Mathematics series, edited by S. Axler, F.W. Gehring, and K.A. Ribet. The second edition includes new material and updates, such as the treatment of the hook formula based on the Novelli-Pak-Stoyanovskii bijection, and a chapter on applications of the first edition's material. The book is intended for graduate students and researchers, with a minimal prerequisite of knowledge of elementary group theory and linear algebra. It includes topics such as group representations, symmetric group representations, combinatorial algorithms, and symmetric functions. The text also discusses applications of symmetric group representations in various areas, including physics, probability, and topology. The book is structured into five chapters, with the first chapter introducing group representations, the second focusing on symmetric group representations, the third on combinatorial algorithms, the fourth on symmetric functions, and the fifth on applications and generalizations. The book includes a bibliography and index, and is accompanied by a list of symbols. The text is written in a clear and accessible style, with detailed explanations and examples.The book "The Symmetric Group: Representations, Combinatorial Algorithms, and Symmetric Functions" is a comprehensive text on the symmetric group, covering representations, combinatorial algorithms, and symmetric functions. It is part of the Graduate Texts in Mathematics series, edited by S. Axler, F.W. Gehring, and K.A. Ribet. The second edition includes new material and updates, such as the treatment of the hook formula based on the Novelli-Pak-Stoyanovskii bijection, and a chapter on applications of the first edition's material. The book is intended for graduate students and researchers, with a minimal prerequisite of knowledge of elementary group theory and linear algebra. It includes topics such as group representations, symmetric group representations, combinatorial algorithms, and symmetric functions. The text also discusses applications of symmetric group representations in various areas, including physics, probability, and topology. The book is structured into five chapters, with the first chapter introducing group representations, the second focusing on symmetric group representations, the third on combinatorial algorithms, the fourth on symmetric functions, and the fifth on applications and generalizations. The book includes a bibliography and index, and is accompanied by a list of symbols. The text is written in a clear and accessible style, with detailed explanations and examples.