Book excerpt: It is well known that classical electrodynamics is riddled with internal inconsistencies springing from the fact that it is a linear, Abelian theory in which the potentials are unphysical. This volume offers a self-consistent hypothesis which removes some of these problems, as well as builds a framework on which linear and nonlinear optics are treated as a non-Abelian gauge field theory based on the emergence of the fundamental magnetizing field of radiation, the B(3) field. Contents: Interaction of Electromagnetic Radiation with One Fermion; The Field Equations of Classical O (3) b Electrodynamics; Origin of Electrodynamics in the General Theory of Gauge Fields; Nonlinear Propagation in O (3) b Electrodynamics: Solitons and Instantons; Physical Phase Effects in O (3) b Electrodynamics; Quantum Electrodynamics and the B (3) Field; Quantum Chaos, Topological Indices and Gauge Theories; Field Theory of O (3) b QED and Unification with Weak and Nuclear Interactions; Potential Applications of O (3) b QED; Duality and Fundamental Problems. Readership: Graduate and undergraduates in physics (electromagnetism), differential geometry & topology, electrical & electronic engineering, theoretical & physical chemistry, chaos and dynamical systems.