As a continuity to Light & Vacuum 2nd Edition, the book Advances in Quantum Electrodynamics Fundamentals consists of a collection of selected papers published in various peer reviewed journals, extended and completed. The link among all these publications is the progressive improvement and refinement of the QED theory fundamentals pertaining the electromagnetic field Hamiltonian, the quantum vacuum, the photon vector potential quantization and the corresponding operator, the photon electric and magnetic fields amplitudes, the photon wave function and finally the relationship to the quantum vacuum. No postulates and no axioms are stated. The whole mathematical developments issue directly from classical and quantum electromagnetic theory drawn on the experimental evidence. A photon quantum equation involving both the first and second quantization of the electromagnetic field, as well as a real photon wave function based on the quantization of the vector potential are established for the first time. The relationship between the electron-positron elementary charge and the single photon vector potential amplitude appears naturally during the second quantization process of the electromagnetic field putting the basis for understanding the physical mechanisms for the mutual transformations: electron + positron <=> gamma photons. Finally, it is shown that photons and particles/antiparticles all issue from the electromagnetic vacuum entailing the introduction of new concepts in particle physics, gravitation and cosmology.