This review is devoted to a discussion of the interpretation of quantum mechanics. The heuristic role and limitations of the principle of observability and of operationalism are discussed. It is shown that the probabilistic approach to quantum mechanics is essential as a way of reconciling the conflicting concepts of particle and wave. The reason why the reduction of the wave packet is not a physical process, but a logical act is explained. The discussion of the paradoxes of quantum mechanics covers many well known examples and includes the Aharonov--Bohm effect and interference between two independent laser beams. It is suggested that the causality principle does not reduce to determinism, but has certain other manifestations too. This is illustrated by the fact that Newtonian mechanics was at one time considered as abstract and impenetrable, in contrast to the ``natural'', but eventually fruitless mechanics of Descartes. It is shown that a classical foundation cannot be provided for quantum mechanics, i.e., it is impossible to introduce hidden variables into quantum mechanics. Mathematical manipulation is reduced to the essential minimum, and many examples are provided to illustrate the discussion. Outstanding contributors to physics are extensively quoted. The review is intended for readers with higher education in both the natural sciences and the humanities, who are interested in conceptual problems in modern science.