Last modified: August 1, 2021
The course text is Differential Geometry: A First Course in Curves and Surfaces, by Theodore Shifrin. The text is short, but correspondingly dense and rich. We'll cover about one section per week.
Read the master: Project Gutenberg has the English translation, by J. C. Morehead and A. M. Hiltebeitel, of General invstigations of curved surfaces by K. F. Gauß.
If you read French (and even if you don't!), you may enjoy Leçons de géométrie supérieure by E. Vessiot. Many of the formulas will look familiar.