Part I- general formalism

1.Actions and equations of motion for free EM, EM coupled to currents and free relativistic particle coupled to EM. EOM from the EM coupled to curved space-time.

2.Symmetries of the EM theory, Noether currents and Noether charges of the full 4d confomral group. Use of symmetries to derive solutions of Maxwell's equations ( boosts and special conformal transformations) 3. The general solution of the free Maxwell theory in the Coulomb (

radiation) gauge and in the covariant gauge 4. Greens functions, general, time independent etc 5. The spherical vector multipole (SVM) solution of the full coupled theory.

Part II-RAdiation

1. The dipole antena comparison of the (SVM) solution the exact solution and the dipole solution.

2. Multipole solution of radiating systems: electric dipole, magnetic dipole and electric quadropole.

3. Energy and angular momentum of radiating systems.

4. Angular dependence of the radiated power 5. The radiation of an accelerated particle, non relativstic and relativstic the angular and frequency dependence. linear and circular accelerators.

6. Radiation due to collisions.

7. Chrenkov radiation

Part III- Em in a non trivial medeia

1. Maxwell's equations in media

2. Energy considarations, Abraham force.

3.Kramers Kroning dispersion relations

4.Transperant matterials, disipative materials, plane waves.

5. From Maxwell's equations to geometrical optics.

6.Non homegeneous, non isotropic materials 7. Effects of non linar dispersion relation.

8. Scattering processes