Translations of Mathematical Monographs Iwanami Series in Modern Mathematics 2003; 254 pp; softcover Volume: 217 ISBN10: 0821827669 ISBN13: 9780821827666 List Price: US$62 Member Price: US$49.60 Order Code: MMONO/217
 Masaki Kashiwara is undoubtedly one of the masters of the theory of \(D\)modules, and he has created a good, accessible entry point to the subject. The theory of \(D\)modules is a very powerful point of view, bringing ideas from algebra and algebraic geometry to the analysis of systems of differential equations. It is often used in conjunction with microlocal analysis, as some of the important theorems are best stated or proved using these techniques. The theory has been used very successfully in applications to representation theory. Here, there is an emphasis on \(b\)functions. These show up in various contexts: number theory, analysis, representation theory, and the geometry and invariants of prehomogeneous vector spaces. Some of the most important results on \(b\)functions were obtained by Kashiwara. A hot topic from the mid `70s to mid `80s, it has now moved a bit more into the mainstream. Graduate students and research mathematicians will find that working on the subject in the twodecade interval has given Kashiwara a very good perspective for presenting the topic to the general mathematical public. Readership Graduate students and research mathematicians. Table of Contents  Basic properties of \(D\)modules
 Characteristic varieties
 Construction of \(D\)modules
 Functorial properties of \(D\)modules
 Regular holonomic systems
 \(b\)functions
 Ring of formal microdifferential operators
 Microlocal analysis of holonomic systems
 Microlocal calculus of \(b\)functions
 Appendix
 Bibliography
 Index
 Index of notations
