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 Maxwell-Lorentz 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? -- Reissner-Nordström solution -- Rotating source: Kerr-Newman solution -- Electrodynamics outside black holes and neutron stars -- Force-free electrodynamics -- Remarks on topology and electrodynamics -- Superconductivity: Remarks on Ginzburg-Landau theory -- Classical (first quantized) Dirac field -- On the quantum Hall effect and the composite fermion -- On quantum electrodynamics -- On electroweak unification -- References -- Author Index.