| Week | Chapters | Topics |
| 1 | 1.1 | Euclidian Space.
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| 2 | 1.2-3 | Tangent Vectors. Directional Derivatives.
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| 3 | 1.4 | Curves in R^3.
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| 4 | 1.5-6 | 1-Forms. Differential Forms.
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| 5 | 1.7 | Mappings.
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| 6 | 2.1 | Dot Product.
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| 7 | 2.2-3 | Midterm Exam. Curves. The Frenet Formulas.
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| 8 | 2.4 | Arbitrary-Speed Curves.
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| 9 | 2.5-6 | Covariant Derivatives. Frame Fields.
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| 10 | 2.7-8 | Connection Forms. The Structural Equations.
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| 11 | 3.1 | Isometries of R^3.
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| 12 | 3.2 | The Tangent Map of an Isometry.
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| 13 | 3.3 | Orientation
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| 14 | 3.4 | Euclidean Geometry
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| 15 | 3.5 | Congruence of Curves. Final Exam.
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