Preface to the second edition (2005)
Preface to the first edition (1981)
Part I. The Synthetic Ttheory: 1. Basic structure on the geometric line
2. Differential calculus
3. Taylor formulae - one variable
4. Partial derivatives
5. Taylor formulae - several variables
6. Some important infinitesimal objects
7. Tangent vectors and the tangent bundle
8. Vector fields
9. Lie bracket
10. Directional derivatives
11. Functional analysis - Jacobi identity
12. The comprehensive axiom
13. Order and integration
14. Forms and currents
15. Currents - Stokes' theorem
16. Weil algebras
17. Formal manifolds
18. Differential forms in terms of simplices
19. Open covers
20. Differential forms as quantities
21. Pure geometry
Part II. Categorical Logic: 1. Generalized elements
2. Satisfaction (1)
3. Extensions and descriptions
4. Semantics of function objects
5. Axiom 1 revisited
6. Comma categories
7. Dense class of generators
8. Satisfaction (2)
9. Geometric theories
Part III. Models: 1. Models for axioms 1, 2, and 3
2. Models for epsilon-stable geometric theories
3. Well-adapted models (1)
4. Well-adapted models (2)
5. The algebraic theory of smooth functions
6. Germ-determined T-infinity-algebras
7. The open cover topology
8. Construction of well-adapted models
9. Manifolds with boundary
10. Field property - germ algebras
11. Order and integration in cahiers topos
Appendices
Bibliography
Index.
