From the reviews: The book deals with the convex geometry of the polyhedral cones CM and related topics ! . With an extensive list of references together with historical notes at the end of each chapter, this book will serve as a welcome comprehensive monograph for research on these rich and fascinating subjects. (T. Oda, Mathematical Reviews, Issue 2010 d) Interactions between convex geometry, ring theory, K-theory, combinatorial geometry, toric geometry, combinatorics in commutative algebra, which are presented in this book together with ! central results in each of the above fields. ! All the chapters contain many useful exercises ! . a good part of the book is not covered by any other book and so especially people from commutative algebra should have it. (Dorin-Mihail Popescu, Zentralblatt MATH, Vol. 1168, 2009) Polytopes, Rings, and K-Theory weighs in at over 400 pages and ten chapters split into three main parts, culminating in the aforementioned K-theory in the given context. ! There are exercises galore in the book ! . All in all, Polytopes, Rings, and K-Theory is an accessible and well-written book on an interesting and important subject ! . It should be quite a success. (Michael Berg, The Mathematical Association of America, December, 2009)