Unlike many other texts on differential geometry, this textbook
also offers interesting applications to geometric mechanics and
general relativity.
The first part is a concise and self-contained introduction to
the basics of manifolds, differential forms, metrics and curvature.
The second part studies applications to mechanics and relativity
including the proofs of the Hawking and Penrose singularity
theorems. It can be independently used for one-semester courses in
either of these subjects.
The main ideas are illustrated and further developed by numerous
examples and over 300 exercises. Detailed solutions are provided
for many of these exercises, making "An Introduction to Riemannian
Geometry" ideal for self-study.
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