Differential Geometry Class Notes
Tensor Geometry: The Geometric Viewpoint and its Uses, by C.T.J. Dodson and T. Poston,
Graduate Texts in Mathematics #130
Springer Verlag (1991).

Copies of the classnotes are on the internet in PDF format as given below. The notes and supplements may contain hyperlinks to posted webpages; the links appear in red fonts. The "Proofs of Theorems" files were prepared in Beamer and they contain proofs of the results from the class notes. The "Printout of Proofs" are printable PDF files of the Beamer slides without the pauses. These notes and supplements have not been classroom tested (and so may have some typographical errors).

  1. Chapter 0. Fundamental Not(at)ions.
  2. Chapter I. Real Vector Spaces.
  3. Chapter II. Affine Spaces.
  4. Chapter III. Dual Spaces.
  5. Chapter IV. Metric Vector Spaces.
  6. Chapter V. Tensors and Multilinear Forms.
  7. Chapter VI. Topological Vector Spaces.
  8. Chapter VII. Differentiation and Manifolds.
  9. Chapter VIII. Connections and Covariant Differentiation.
  10. Chapter IX. Geodesics.
  11. Chapter X. Curvature.
  12. Chapter XI. Special Relativity.
  13. Chapter XII. General Relativity.

Chapter II. Affine Spaces.

Chapter III. Dual Spaces.

Chapter IV. Metric Vector Spaces.

Chapter V. Tensors and Multilinear Forms.

Chapter VI. Topological Vector Spaces.

Chapter VII. Differentiation and Manifolds.

Chapter IX. Geodesics.

Chapter X. Curvature.

Other Notes on Differential Geometry and Relativity
Faber's Differential Geometry Book
Differential Geometry
A Course in Differential Geometry
Differential Geometry
(in preparation)
Robert M. Wald's General Relativity
General Relativity
(in preparation)
Hawking and Ellis' Large Scale Structure of Space-time
General Relativity
(in preparation)

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