World – Universe Model is based on three primary assumptions: 1) The World is finite and is expanding inside the Universe with speed equal to the electrodynamic constant c. The Universe serves as an unlimited source of energy that continuously enters into the World from the boundary. 2) Medium of the World, consisting of protons, electrons, photons, neutrinos, and dark matter particles, is an active agent in all physical phenomena in the World. 3) Two fundamental parameters in various rational exponents define all macro and micro features of the World: Fine-Structure Constant α, and dimensionless quantity Q. While α is constant, Q increases with time, and is in fact a measure of the size and the age of the World. The World – Universe Model explains experimental data accumulated in the field of Cosmology over the last decades: the size and age of the World; critical energy density and the gravitational parameter; temperatures of the cosmic microwave background radiation and black body radiation of cosmic dust; fractal structure of the World and its evolution; observed expansion of the World and cosmological redshift. Additionally, the Model makes predictions pertaining to masses of dark matter particles, photons, axions, and neutrinos; proposes new types of particle interactions (Super Weak and Extremely Weak) and the fundamental physical parameters of the World; gives a new “low density small white dwarf” model of Ball Lightning and dineutrino model of Extreme Ball Lightning based on super weak interaction; explains “Pioneer Anomaly”; and resolves paradoxes like “Matter – Antimatter Asymmetry” and “Faint Young Sun”. The Model proposes to introduce a new fundamental parameter Q in the CODATA internationally recommended values for calculating time dependent parameters of the World. Keywords: World – Universe Model, Fractal Cosmology, Fine-Structure Constant, Dark Matter, Microwave Background Radiation, Maxwell-Lorentz Equations, Dirac’s Equations, Fractal Particle Structure, Grand Unified Theory, Ball Lightning, CODATA