A recently developed approach to calculus lets Bell go very quickly from the basic definitions up to several interesting applications in geometry and mechanics. This version of calculus bypasses a lot of technical details  to focus on the geometric meaning. If you have had analytic geometry then  in principle you could read this book. It would be better if you have had  some exposure to calculus but you do not need to remember much of it, and  this book can quickly take you farther.<br>Readers who want to get to the  applications can skim through much of the first chapter, on historical and  philosophic motivations for the approach.<br>But a word for specialists:  the book is also valuable as an exploration of this approach, called  "synthetic differential geometry". This was created to make  calculus more accessible but most people writing about it have focussed on  theoretical investigations, as it involves a number of very new ideas. By  writing on the introductory level, with rather advanced geometric  applications, Bell has brought out novel aspects of the approach. Logicians  and mathematicians interested in this foundation for geometry, or in  elementary topos theory, should see what he has done.