Electrodynamics of moving bodies: Systematic foundation of EM theory

This is a brief presentation of EM theory, as the well-elaborated electrodynamics of moving bodies. Apart from the standard differential equations, some algebraic relations, complementary in the sense and application, are affirmed. The field transformations, completed by these relations, simultaneously treat transverse and longitudinal directions. Relativistic kinematics and respective opinions, based on the incomplete transformations, are thus convincingly surpassed.