Discrete, Finite and Lie Groups : Comprehensive Group Theory in Geometry and Analysis

In a self contained and exhaustive work the author covers Group Theory in its multifaceted aspects, treating its conceptual foundations in a proper logical order. First discrete and finite group theory, that includes the entire chemical-physical field of crystallography is developed self consistently, followed by the structural theory of Lie Algebras with a complete exposition of the roots and Dynkin diagrams lore. A primary on Fibre-Bundles, Connections and Gauge fields, Riemannian Geometry and the theory of Homogeneous Spaces G/H is also included and systematically developed.

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"This beautiful book offers a thorough and cohesive presentation of group theory and related concepts, which lie at the core of modern natural sciences and engineering, and whose relevance nowadays extends even to social sciences. As the author argues, the topic of group theory should be an essential part of scientific education, and should be taught aiming to a high degree of abstraction: this is reflected in the structure of this book, which starts from simple notions and progressively moves towards deeper, more abstract and mathematically more powerful concepts. The text is characterized by the unique style of its author: a style that is mathematically very rigorous but at the same time also highly enjoyable, with occasional historical references and enlightening examples. A must read." Prof. Marco Panero, University of Turin, Department of Physics