Pedagogical presentation and analysis of the symmetry aspects of physical systems in terms of group theoretical concepts and methodology has been evolving over the past six or seven decades, since the pioneering textbooks by Weyl and Wigner first appeared. This constantly evolving pedagogy has resulted in over a hundred textbooks on the subject. The impetus behind these efforts has stemmed from the general recognition of the invaluable role that the application of such methodology plays in determining and predicting the properties of a physical system.

Symmetry concepts provide a very useful means for systematizing the description of a physical system in terms of its energy and momentum, and other relevant physical quantities. Furthermore, the incipient methodologies furnish a very efficient framework for classifying its physical states, and a crucial machinery for simplifying the intervening numerical applications of physical laws. By means of the irreducible representations of its symmetry group, one can classify physical states and particles in a logical way and establish selection rules, which predict restrictions on possible transitions between different physical states. The use of symmetry also simplifies numerical calculations, for example, in solving the Schrö equation for condensed matter systems. Moreover, from the symmetry properties of a physical system, one can make conclusions about the values of measurable physical quantities, and, conversely, one can trace a symmetry group of a system from observed regularities in measured quantities. There is also an intimate connection between symmetry, invariance and dynamical laws.