Journal of Physical Sciences Successes, 1964, t. LXXXIII, vol. 4. Translated by E. Winger, Symmetry and Conservation Laws, Physics Today 17, 34 (1964). Questions of symmetry, invariance, and conservation laws have played an important role in the thinking of physicists since Galileo and Newton, and perhaps before. However, in classical mechanics, these questions were not of a fundamental nature, and even more so, did not lie at its basis. Einstein for the first time in a bright and distinct form expressed postulates about the symmetry of space, about the equivalence of directions and points of space, as well as the equivalence of moving and resting coordinate systems. In connection with the Bohr model of the atom, the theorem on the conservation of momentum became crucial. Moreover, as early as 1904, Hamel established a fundamental relationship between conservation laws and the basic symmetries of space and time. Events, laws of nature, principles of invariance . Geometric and dynamic principles of invariance. Geometric principles and conservation laws . Dynamic principles of invariance . Bibliography (23 titles).