These are the notes of my talk about Morse theory in the seminar same-named seminar organized by Prof. Dr. S. Sabatini at the university of Cologne. Morse theory is the study of the relations between functions on a space and the shape of the space. In this short introduction we will follow the excellent book of Yukio Matsumoto[1]. Since this is just a short introduction it covers only the first part of the book which deals only with the case of two dimensional spaces, i.e. surfaces.

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