Analog radar signal design and digital signal processing -a Heisenberg nilpotent Lie group approach -- Fourier optics from the perspective of the Heisenberg group -- Lie series, Lie transformations, and their applications -- Foundations of a Lie algebraic theory of geometrical optics -- Canonical transforms for paraxial wave optics -- Wave theory of imaging systems -- Invariants and coherent states in fiber optics -- The influence of spherical aberration on gaussian beam propagation.