*Editor's note: This review covers both *Mathematical Physiology I: Cellular Physiology* and *Mathematical Physiology II: Systems Physiology.

Since its original release in 1998, many have viewed the first edition of *Mathematical Physiology *as the best book ever written on the subject. The first edition provides students, faculty, and researchers with excellent resources for studying cellular and system physiology. It is a single volume text tailored to advanced students and researchers primarily interested in understanding how mathematics can be used to answer physiological questions and how physiological problems can lead to new mathematical discoveries.

By the authors’ own admission, a single text on mathematical physiology cannot be an all-inclusive summary of the field. With the introduction of the second edition, the authors have expanded their discussion of fundamental models and principles into a two-volume set. Even in two volumes experts in the field may encounter omissions, but for the majority of readers, the texts provide a comprehensive summary of the important concepts in mathematical physiology.

From a mathematical perspective, both editions cover many advanced topics such as ordinary differential equations, dynamical systems, perturbation methods, partial differential equations, and stochastic processes. The authors clearly state that the goals of the book are not to introduce mathematical concepts in the framework of physiology, but rather to use mathematics to explain certain physiological concepts. In order to make the material a little more accessible to readers, the second edition includes new appendices and sections devoted to explaining the mathematical content. For example, a Math Background Appendix has been included in Chapter 1 and points the reader to resources and texts on different topics. Another Appendix is devoted to Stochastic Processes including Markov processes. Although these were not included in the first edition, their inclusion here by no means is meant to replace a course or individual texts on the subjects.

For those new to mathematical physiology, the first edition is probably still a better choice to give you an introduction and reference point; it has plenty of information, mathematical models and resources and these are all included in one book. For those actively working in the field of mathematical physiology who already use the first edition, the two-volume set is a must have. The new edition includes updated descriptions, new models, and new figures adding to the breadth of the first edition. One of the most beneficial aspects of the two-volume set is the addition of about a decade’s worth of work and references (over 350!). I also found that the exercises were adjusted to include questions on the new material and in some cases both routine and more advanced questions were added giving more flexibility when used as a course textbook.

As someone who references the first edition frequently, I was excited to see the arrival of the second edition. I was pleased to find that the authors did not just change a few paragraphs for the second edition, but really delved into new topics, updated references, and expanded on the original.

Joe Latulippe (jjlatulippe@csupomona.edu) is an assistant professor of mathematics at Cal Poly Pomona. He is a Project NExT Fellow (Sun Dot ’07), and is interested in mathematical biology and modeling. In his free time, Joe trains in Aikido (a non-violent Japanese martial art), and enjoys painting landscapes and drawing.