1. Classical and Quantum Optics: Vector Field Equations (Maxwell) and Quantum Electrodynamics, with applications in nearfield optics, nanooptics, photonics, metamaterials and other optical devices. 2. Quantum Magnetism, Quantum ManyBody/Field Theory, Quantum Statistical Mechanics and Quantum Phase Transitions: The 4spinor Dirac equation and its semirelativistic limit in the presence of external electromagnetic fields, with applications in metalinsulator transitions and magnetic phase transitions involving complex materials. 3. Nonequilibrium Statistical Mechanics: Quantum Scattering, Boltzmann Transport Theory and Continuous Phase Transitions, with applications on ion transport (drift and diffusion) in complex biological systems.