The mathematical elegance of the theory of quantum mechanics and the crucial conceptual problems arising from it are most fascinating. The well-known books of Dirac¹ and of von Neumann² are most useful if one tries to "understand" what is meant by the "physical interpretation" of quantum mechanics. Concerning the problem of the measuring process, Heisenberg's book Die physikalischen Prinzipien der Quantentheorie ³ is very fundamental. The beauty of the mathematical structure of quantum mechanics can be felt by studying the books of Wigner⁴, van der Waerden⁵ and Weyl⁶, which also describe the connection between group theory and quantum mechanics. Although group-theoretical methods are essential for a logical construction of quantum mechanics (e.g. the representations of the Galilei-group in non-relativistic quantum mechanics), I would like to discuss here the problems of the foundation of quantum mechanics only.