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...