Abstract
These notes are designed to give a heuristic guide to many of the basic constructions of differential geometry. They are by no means complete; nor are they at all exhaustive. Some of the elementary topics which would be covered by a more complete guide are: geodesics and conjugate points; Lie derivative and the flow of a vector field; coordinate construction techniques; GauB-Bonnet Theorem; Bochner formulae; de Rham cohomology; Lie groups. Despite these and other omissions, I hope that the notes prove useful in motivating the basic geometric constructions on a manifold.
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