1. The Economic Framework.- 2. Introduction to the Mathematics.- 3. Differentiable Manifolds and Mappings, Tangents, Vectorfields.- 4. Regular Equilibria. A First Approach.- 5. Scarf's Example.- 6. Excess Demand Functions.- 7. Debreu's Theorem on the Finiteness of the Number of Equilibria of an Economy.- 8. Continuity of the Walras Correspondence for C Demand Functions.- 9. Density of Transversal Intersection.- 10. Regular Economies.- 11. Stability Questions and the Number of Equilibria.- 12. Large Economies.- Some Standard Notation.- References.