Starting at an introductory level, the book leads rapidly to
important and often new results in synthetic differential geometry.
From rudimentary analysis the book moves to such important results
as: a new proof of De Rham's theorem; the synthetic view of global
action, going as far as the Weil characteristic homomorphism; the
systematic account of structured Lie objects, such as Riemannian,
symplectic, or Poisson Lie objects; the view of global Lie algebras
as Lie algebras of a Lie group in the synthetic sense; and lastly
the synthetic construction of symplectic structure on the cotangent
bundle in general. Thus while the book is limited to a naive point
of view developing synthetic differential geometry as a theory in
itself, the author nevertheless treats somewhat advanced topics,
which are classic in classical differential geometry but new in the
synthetic context. Audience: The book is suitable as an
introduction to synthetic differential geometry for students as
well as more qualified mathematicians.
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