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)

• I Cones, monoids, and triangulations.- Polytopes, cones, and complexes.- Affine monoids and their Hilbert bases.- Multiples of lattice polytopes.- II Affine monoid algebras.- Monoid algebras.- Isomorphisms and automorphisms.- Homological properties and Hilbert functions.- Gr#x00F6;bner bases, triangulations, and Koszul algebras.- III K-theory.- Projective modules over monoid rings.- Bass#x2013;Whitehead groups of monoid rings.- Varieties.