Dirk Struik’s *Lectures in Classical Differential Geometry*, first published in 1950, was the text I used in my first course in the subject in 1960. It is one of the main reasons I became a differential geometer. I especially appreciated the images, culled from many different sources, as well as the historical placement of the geometric discoveries. Although I was a bit confused at the time by the many different notations that showed up in the exercises taken from various sources, I realized later that multiple representations are a feature of the development of the subject, giving rise to the comical characterization: “Differential geometry is the study of properties invariant under change of notation.”

The book now listed in MAA Reviews is the second edition, published in 1961. It is even more valuable since it includes an appendix on “The Method of Pfaffians” which more aptly for present-day readers might be titled “Classical Differential Geometry from the Point of View of Differential Forms.” As such, the book now gives an introduction of the subject that leads into modern treatments such as the one preferred by my advisor, Shiing-Shen Chern, in his prize-winning essay on global differential geometry.

This relatively short book contains a concise introduction to a number of classical topics that are still important today. A wealth of exercises help the reader see the historical development of the subject and set the scene for modern investigations. The Dover paperback version makes this resource accessible to any student or school library and its placement on the list of essential books in mathematics is well deserved.

Thomas F. Banchoff is Professor of Mathematics at Brown University and a former president of the MAA.