Mathematics

I. Clifford Algebras and Dirac Operators.- 1. Clifford Algebras and Clifford Modules.- 2. Clifford Bundles and Compatible Connections.- 3. Dirac Operators.- 4. Dirac Laplacian and Connection Laplacian.- 5. Euclidean Examples.- 6. The Classical Dirac (Atiyah-Singer) Operators on Spin Manifolds.- 7. Dirac Operators and Chirality.- 8. Unique Continuation Property for Dirac Operators.- 9. Invertible Doubles.- 10. Glueing Constructions. Relative Index Theorem.- II. Analytical and Topological Tools.- 11. Sobolev Spaces on Manifolds with Boundary.- 12. Calderon Projector for Dirac Operators.- 13. Existence of Traces of Null Space Elements.- 14. Spectral Projections of Dirac Operators.- 15. Pseudo-Differential Grassmannians.- 16. The Homotopy Groups of the Space of Self-Adjoint Fredholm Operators.- 17. The Spectral Flow of Families of Self-Adjoint Operators.- III. Applications.- 18. Elliptic Boundary Problems and Pseudo-Differential Projections.- 19. Regularity of Solutions of Elliptic Boundary Problems.- 20. Fredholm Property of the Operator AR.- 21. Exchanges on the Boundary: Agranovi?-Dynin Type Formulas and the Cobordism Theorem for Dirac Operators.- 22. The Index Theorem for Atiyah-Patodi-Singer Problems.- 23. Some Remarks on the Index of Generalized Atiyah-Patodi-Singer Problems.- 24. Bojarski's Theorem. General Linear Conjugation Problems.- 25. Cutting and Pasting of Elliptic Operators.- 26. Dirac Operators on the Two-Sphere.