This is a nicely readable textbook on differential geometry. It offers an outstanding, comprehensive presentation of both theoretical and computational aspects. All 27 chapters are accompanied by Mathematica code in the form of Mathematica notebooks in the appendix (the code can be downloaded from the publisher’s web site). This approach enables the reader to better understand how to define and compute standard geometric functions and how to construct new curves and surfaces from existing ones. Moreover, work with Mathematica notebooks may serve as a natural way of acquiring the basic and intermediate knowledge of Mathematica by example. There are hundreds of illustrations that help the reader visualize the concepts. Throughout the book the reader will find biographical information about 75 scientists, most of them with small portraits. It is a nicely written book, strongly recommended to all with an interest in differential geometry, its computational aspects and related fields.