Lectures on Classical Differential Geometry: Second Edition
Dirk J. Struik
Dover Publications
With this book, I hope I have finally broken the code and reached a critical mass in advanced mathematical understanding. These Dover Series books allow "it all to hang out." It is "old school" in the best sense of that phrase: that is, in the sense that they do no "sugar coat" their explanations. They do not "dumb it down" or "fancy it up to" ease the pain. One knows what one is up against when one picks up a book from the "Dover Series." They are always clean and sparse in their explanations.

In this regard, this book is no exception. Professor Struik begins at the beginning and goes straight through to the end without skipping any steps and without passing go to collect his $200. He gives the fundamental conceptions of the theory of curves and surfaces, introducing all of the machinery necessary to understand them in a graduated fashion suitable only to the requirements of the topic itself. Elementary calculus will serve the reader well, especially with a smattering of Linear Algebra thrown in. The author wastes no time with sexy side issues or superfluous explanations: Just the basic facts of the fundamental elements here. Those looking for more advanced topics, should consult those books that use this one as their background.

Explanations are sparse, but never deficient; the same is true of the equations. Notation is straightforward and always clear and economical. It is easy to see that  (and why) other books on the same topic have used this one as background, but oddly, those other books have been unable to improve upon this one. Other than the fact that the graphics need updating, and more modern topics are missing, this is a splendid effort. Just what I needed.

Five Stars.