Physical symmetries and a structure of transformations

Lie groups and Lie algebras are briefly introduced to study the invariance groups of symmetry transformations. The role of invariance principles is studied briefly and the fact that they are accompanied by invariance groups is brought out. It is seen that Lie algebras, infinitesimal groups of invariance transformations, provide a common formalism of dynamical theories through proper realizations confirming the argument that an invariance group characterizes a physical theory. Throughout the discussion, an analogy between a geometry and a physical theory, existing due to the fact that both are relational systems, is made.