The theory of Gröbner bases is a main tool for dealing with rings of
differential operators. This book reexamines the concept of Gröbner
bases from the point of view of geometric deformations. The algorithmic
methods introduced in this book are particularly useful for studying the
systems of multidimensional hypergeometric PDE's introduced by Gelfand,
Kapranov, and Zelevinsky. A number of original research results are
contained in the book, and many open problems are raised for future
research in this rapidly growing area of computational mathematics.