Preface y. - Five plus one axioms. - Topological approach. - Electromagnetic spacetime relation as fifth axiom. - Electrodynamics in matter and the sixth axiom. - List of axioms. - A reminder: Electrodynamics in 3-dimensional Euclidean vector calculus. - On the literature. - References. - A Mathematics: Some Exterior Calculus. - Why exterior differential forms?. - A. 1 Algebra. - A. 2 Exterior calculus. - A. 3 Integration on a manifold. - References. - B Axioms of Classical Electrodynamics. - B. 1 Electric charge conservation. - B. 2 Lorentz force density. - B. 3 Magnetic flux conservation. - B. 4 Basic classical electrodynamics summarized example. - B. 5 Electromagnetic energy-momentum current and action. - References. - C More Mathematics. - C. 1 Linear connection. - C. 2 Metric. - References. - D The MaxwellLorentz Spacetime Relation. - D. 1 A linear relation between H and F. - D. 2 Propagation of electromagnetic waves: Quartic wave surface. - D. 3 First constraint: Electric/magnetic reciprocity. - D. 4 Second constraint: Vanishing skewon field. Emergence of the light cone. - D. 5 Extracting the metric by an alternative method. - D. 6 Fifth axiom: Maxwell-Lorentz spacetime relation. - References. - E Electrodynamics in Vacuum and in Matter. - E. 1 Standard Maxwell-Lorentz theory in vacuum. - E. 2 Electromagnetic spacetime relations beyond locality and linearity. - E. 3 Electrodynamics in matter constitutive law. - E. 4 Electrodynamics of moving continua. - References. - Outlook. - How does gravity affect electrodynamics?. - ReissnerNordström solution. - Rotating source: KerrNewman solution. - Electrodynamics outside black holes and neutron stars. - Force-free electrodynamics. - Remarks on topology and electrodynamics. - Superconductivity: Remarks on GinzburgLandau theory. - Classical (first quantized) Dirac field. -On the quantum Hall effect and the composite fermion. - On quantum electrodynamics. - On electroweak unification. - References. - Author Index. Language: English