This book provides a systematic presentation of the mathematical
foundation of modern physics with applications particularly within
classical mechanics and the theory of relativity. Written to be
self-contained, this book provides complete and rigorous proofs of
all the results presented within. Among the themes illustrated 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. It can be used as a textbook for a pure mathematics
course in differential geometry, assuming the reader has a good
understanding of basic analysis, linear algebra and point set
topology. The book will also appeal to students of theoretical
physics interested in the mathematical foundation of the theories.
General
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