Physical symmetry and geometrical symmetry -- On symmetries associated with Hamiltonian dynamics -- One-parameter transformation groups -- Everywhere : local invariance -- Lie transformation groups and Lie algebras -- Dynamical symmetry in Hamiltonian mechanics -- Symmetries of classical Kepler motion -- Dynamical symmetry in Schrödinger quantum mechanics -- Spectrum-generating Lie algebras and groups admitted by Schröedinger equations -- Dynamical symmetry of regularized hydrogen-like atoms -- Uncovering approximate dynamical symmetries : examples from atomic and molecular physics -- Rovibronic systems -- Dynamical symmetry of Maxwell’s equations.