This note explains the following
topics: From Kock–Lawvere axiom to microlinear spaces, Vector
bundles,Connections, Affine space, Differential forms, Axiomatic structure of
the real line, Coordinates and formal manifolds, Riemannian structure,
Well-adapted topos models.

This
note contains on the following subtopics of Differential Geometry,
Manifolds, Connections and curvature, Calculus on
manifolds and Special topics.

This note contains on the following subtopics
of Symplectic Geometry, Symplectic Manifolds,
Symplectomorphisms, Local
Forms, Contact Manifolds, Compatible Almost Complex Structures, Kahler
Manifolds, Hamiltonian Mechanics, Moment Maps, Symplectic Reduction, Moment Maps
Revisited and Symplectic Toric Manifolds.

These notes are an attempt to
summarize some of the key mathematical aspects of differential geometry,as they
apply in particular to the geometry of surfaces in R3. Covered topics are: Some
fundamentals of the theory of surfaces, Some important parameterizations of
surfaces, Variation of a surface, Vesicles, Geodesics, parallel transport and
covariant differentiation.

This note
covers the following topics: Linear Algebra, Differentiability, integration,
Cotangent Space, Tangent and Cotangent bundles, Vector fields and 1 forms,
Multilinear Algebra, Tensor fields, Flows and vectorfields, Metrics.

This book is a monographical work on
natural bundles and natural operators in differential geometry and this book
tries to be a rather comprehensive textbook on all basic structures from the
theory of jets which appear in different branches of differential geometry.

Author(s): Ivan
Kolar, Jan Slovak and Peter W. Michor

This book covers the following topics: Smooth Manifolds, Plain curves, Submanifolds, Differentiable maps, immersions,
submersions and embeddings, Basic results from Differential Topology, Tangent
spaces and tensor calculus, Riemannian geometry.