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The author presents the extension of differential geometry from curves and surfaces to manifolds in general. It provides a broad introduction to the field of differentiable and Riemannian manifolds, tying together classical and modern formulations. The goal is to introduce manifolds in a both streamlined and mathematically rigorous way.
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The author presents the extension of differential geometry from curves and surfaces to manifolds in general. It provides a broad introduction to the field of differentiable and Riemannian manifolds, tying together classical and modern formulations. The goal is to introduce manifolds in a both streamlined and mathematically rigorous way.