As I continue preparing for a differential geometry course that might not run, I am assembling a bibliography for my students. (It is far too sad to contemplate that the course won’t run. I will just Keep Calm and Continue Planning.)

I want to hand them an *annotated* bibliography, with some reasonable commentary about the quality, content and outlook of the texts on the list.

This job is turning out to be a rather large one. There are

*lots*of elementary differential geometry texts. Not quite as many as calculus or linear algebra, but still.

So I will break the job into some more manageable pieces. I’ll start with a simple book list. These are the fruits of an afternoon’s search for possible introductory texts. Later, I will fill in with miniature reviews of the books as I take a more detailed look at them. I have every intention of starting this project strong and then watching it slowly fade into a guilty state of incompletion. But who knows? Maybe this is actually something I can finish.

### The Great Elementary Differential Geometry Textbook Review of Winter 2012

A note on the definition of “elementary”: I will only consider texts that I think have some outside chance of serving as a stand-alone introduction to the classical differential geometry of curves and surfaces in . The prerequisites should be no more than courses in multivariable calculus and linear algebra. A few books presuppose a passing familiarity with differential equations. I will allow this, but if the text assumes material past what might reasonably be covered in the course of the regular calculus sequence it will be removed from the list.

I have cut out many books simply because they are too advanced. When I am done with the list of elementary books, I will likely include a short list of my favorite “advanced books” and some other reference material I think is interesting.

I found over 20 books without much effort, so this might take a bit of work.

### The List

In no particular order, the books I will look at are:

- Stoker,
*Differential Geometry* - Wardle,
*Differential Geometry* - Kreyszig,
*Differential Geometry* - Willmore,
*An Introduction to Differential Geometry* - Struik,
*Lectures on Classical Differential Geometry* - O’Neill,
*Elementary Differential Geometry* - Oprea,
*Differential Geometry and its Applications* - Snygg,
*A New Approach to Differential Geometry Using Clifford’s Geometric Algebra* - Pressley,
*Elementary Differential Geometry* - Toponogov,
*Differential Geometry of Curves and Surfaces* - Thorpe,
*Elementary Topics in Differential Geometry* - McCleary,
*Geometry from a Differential Viewpoint* - Kühnel,
*Differential Geometry: Curves – Surfaces – Manifolds, 2nd Ed.* - Bär,
*Elementary Differential Geometry* - Montiel & Ros,
*Curves and Surfaces, 2nd Ed.* - Millman & Parker,
*Elements of Differential Geometry* - do Carmo,
*Differential Geometry of Curves and Surfaces* - Banchoff and S. Lovett,
*Differential Geometry of Curves and Surfaces* - Gray,
*Modern Differential Geometry of curves and Surfaces with Mathematica* - Vaizman,
*A First Course in Differential Geometry* - Spivak,
*A Comprehensive Introduction to Differential Geometry, vols 1-5* - Shifrin,
*Differential Geometry: A First Course in Curves and Surfaces* - Henderson,
*Differential Geometry: A Geometric Introduction* - Weatherburn,
*Differential Geometry of Three Dimensions*

There are a couple of other texts, I suppose. I found these by going through major publishers websites and looking through UNI’s Rod Library stacks. A few of these have been on my shelf for a while, but I haven’t really taken time to read some significant portion and decide if I like them.

Have I mentioned that I have a problem? Yeah, I spend too much money on mathematics books.