This paper provides an overview of the Hypersphere World – Universe Model (WUM). WUM unifies and simplifies existing cosmological models and results into a single coherent picture, and proceeds to discuss the origin, evolution, structure, ultimate fate, and primary parameters of the World. WUM explains the experimental data accumulated in the field of Cosmology and Astroparticle Physics over the last decades: the age of the World and critical energy density; the gravitational parameter and Hubble’s parameter; temperatures of the cosmic microwave background radiation and the peak of the far-infrared background radiation; gamma-ray background and cosmic neutrino background; macrostructure of the World and macroobjects structure. Additionally, the Model makes predictions pertaining to masses of dark matter particles, photons, and neutrinos; proposes new types of particle interactions (Super Weak and Extremely Weak); shows inter-connectivity of primary cosmological parameters of the World and the rise of the solar luminosity during the last 4.6 Byr. The Model proposes to introduce a new fundamental parameter Q in the CODATA internationally recommended values.