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.

In winter 71/72 I held a seminar on general equilibrium theory for a jOint group of students in mathematics and in econo­ mics at the university of Bonn , w.Germany1~ The economists , how­ ever , had a mathematical background well above the average • Most of the material treated in that seminar is described in these notes. The connection between smooth preferences and smooth demand func­ tions [ see Debreu (1972) ] and regular economies based on agents with smooth preferences are not presented here • Some pedagogical difficulties arose from the fact that elementary knowledge of algebraic topology is not assumed although it is helpful and indeed necessary to make some arguments precise • It is only a minor restriction , at present , that functional ana­ lysis is not used • But with the development of the theory more economic questions will be considered in their natural infinite dimensional setting • Economic knowledge is not required , but especially a reader without economic background will gain much by reading Debreu's classic "Theory of Value" (1959) • Although the formulation of our economic problem uses a map between Euclidean spaces only , we shall also consider ma- folds • Manifolds appear in our situation because inverse images under differentiable mappings between Euclidean spaces are very often differentiable manifolds • ( Under differentiability assump­ tions , for instance , the graph of the equilibrium set correspon­.