Riemannian geometry has today become a vast and important subject.
This new book of Marcel Berger sets out to introduce readers to
most of the living topics of the field and convey them quickly to
the main results known to date. These results are stated without
detailed proofs but the main ideas involved are described and
motivated. This enables the reader to obtain a sweeping panoramic
view of almost the entirety of the field. However, since a
Riemannian manifold is, even initially, a subtle object, appealing
to highly non-natural concepts, the first three chapters devote
themselves to introducing the various concepts and tools of
Riemannian geometry in the most natural and motivating way,
following in particular Gauss and Riemann.
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