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...