This book provides a systematic presentation of the mathematical foundation of modern physics with applications particularly within classical mechanics and the theory of relativity. Among the themes presented in the book are differentiable manifolds, differential forms, fiber bundles and differential geometry with non-trivial applications especially within the general theory of relativity. The emphasis is upon a systematic and logical construction of the mathematical foundations. The book is self contained with definitions, theorems and detailed proofs. The book will also appeal to students of theoretical physics interested in the mathematical foundation of the theories.
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