The book is devoted to the mathematical foundations of nonextensive statistical mechanics. This is the first book containing the systematic presentation of the mathematical theory and concepts related to nonextensive statistical mechanics, a current generalization of Boltzmann-Gibbs statistical mechanics introduced in 1988 by one of the authors and based on a nonadditive entropic functional extending the usual Boltzmann-Gibbs-von Neumann-Shannon entropy. Main mathematical tools like the q-exponential function, q-Gaussian distribution, q-Fourier transform, q-central limit theorems, and other related objects are discussed rigorously with detailed mathematical rational. The book also contains recent results obtained in this direction and challenging open problems. Each chapter is accompanied with additional useful notes including the history of development and related bibliographies for further reading.Key FeaturesThis is the first book where mathematical foundations of the novel theory of nonextensive statistical mechanics are systematically presented in great detailThe book is rich of novel ideas and applications to various practical problems arising in natural and social sciences, as well as medicine and engineering. Researchers may benefit adapting the ideas to their own research and developing relevant approaches. The book also contains discussions on some important open problems the solutions of which would be a significant contribution to statistical mechanics in generalThe book is accessible for graduate students and for beginning researchers. The established researchers also can benefit from the book since the novel ideas and results are presented within in a pedagogical order

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