ABSTRACT
In the middle of 17-th Century the French mathematician Fermat introduced the variational principle of geometrical optics. Behind this principle is the beautiful notion that Nature always chooses the simplest and easiest way to act. Three centuries later, following work by such outstanding scientists as Maupertuis, Euler, Lagrange, and Hamilton, this idea has become one of the main tools in the investigation of Nature. These days there is no doubt that the variational principle and the action formalism reflect a deep property of Nature. For a long time, however, in spite of some of the great work that had been done on this concept, it was considered an abstract mathematical construction.
