*Frontmatter, pg. i*Contents, pg. v*Introduction, pg. 1*CHAPTER 1. Results from Representation Theory, pg. 9*CHAPTER 2. D.E.'s and D-modules, pg. 31*CHAPTER 3. The Generalized Hypergeometric Equation, pg. 92*CHAPTER 4. Detailed Analysis of the Exceptional Cases, pg. 122*CHAPTER 5. Convolution of D-modules, pg. 161*CHAPTER 6. Fourier Transforms of Kummer Pullbacks of Hypergeometrics, pg. 178*CHAPTER 7. The l- adic Theory, pg. 193*CHAPTER 8. l-adic Hypergeometrics, pg. 251*CHAPTER 9. G2 Examples, Fourier Transforms, and Hypergeometrics, pg. 320*CHAPTER 10. l -adic Exceptional Cases, pg. 332*CHAPTER 11. Reductive Tannakian Categories, pg. 352*CHAPTER 12. Fourier Universality, pg. 363*CHAPTER 13. Stratifications and Convolution, pg. 384*CHAPTER 14. The Fundamental Comparison Theorems, pg. 402*References, pg. 425