From the reviews: "This book brings together several areas of mathematics that have developed mostly independently over the past 30 years. ... the book is self-contained. ... provide an illuminating class of examples, which are investigated throughout the book. The writing is consistently clear, with careful attention paid to detail. ... the determined reader will find it an ultimately rewarding read, and certainly worth the effort." (Alexander I. Suciu, Mathematical Reviews, Issue 2011 m) "This book revisits the paper of Dahmen and Micchelli and reproves some of their results ... by different methods. ... The book is written at a relatively elementary level ... . A motivated reader will find it well worth the effort." (G. K. Sankaran, Zentralblatt MATH, Vol. 1217, 2011)

• Preliminaries.- Polytopes.- Hyperplane Arrangements.- Fourier and Laplace Transforms.- Modules over the Weyl Algebra.- Differential and Difference Equations.- Approximation Theory I.- The Di?erentiable Case.- Splines.- RX as a D-Module.- The Function TX.- Cohomology.- Differential Equations.- The Discrete Case.- Integral Points in Polytopes.- The Partition Functions.- Toric Arrangements.- Cohomology of Toric Arrangements.- Polar Parts.- Approximation Theory.- Convolution by B(X).- Approximation by Splines.- Stationary Subdivisions.- The Wonderful Model.- Minimal Models.