The following are notes of lectures held at the University of Vienna in 1975/76 and at the University of Linz in February 1976. There the main part of these notes has been written and revised by Prof. J. B. Cooper, who also invited me to Linz. I thank him and the other members of the enthusiastic and inspiring audience at Linz who helped to bring the presentation into a somewhat final form. The notes were multiplied with the title: Classification of elementary catastrophes of codimension ^ 6. Institutsbericht Nr. 51 of Johannes Kepler UniversitHt Linz, Institut far Mathematik. 1976. After that I received letters of D, Siersma and Tim Poston, pointing out mistakes. The lectures were next given at the University of. Klagenfurt in 1977/78, where also a multiplied version of the-(corrected) notes appeared under the title: Elementary catastrophe theory. Institut fUr Mathematik, UniversitBt fOr Bildungswissenschaften, Klagenfurt, 1978. Then the lectures were held at the University of Mannheim in 1979, where §10 was added.

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