Hypersphere World-Universe Model (WUM) is the only cosmological model in existence that is consistent with the Law of Conservation of Angular Momentum. To be consistent with this Fundamental Law, WUM discusses in detail the Beginning of the World. The Model introduces Dark Epoch (spanning from the Beginning of the World for 0.4 billion years) and Luminous Epoch (ever since for 13.8 billion years). Big Bang discussed in Standard Cosmology is, in our view, transition from Dark Epoch to Luminous Epoch due to Rotational Fission of Overspinning Dark Matter (DM) Supercluster’s Cores and self-annihilation of Dark Matter Particles (DMPs). WUM envisions Matter carried from the Universe into the World from the fourth spatial dimension by DMPs. Luminous Matter is a byproduct of DM self-annihilation. WUM solves a number of physical problems in contemporary Cosmology and Astrophysics through DMPs and their interactions: Angular Momentum problem in birth and subsequent evolution of Galaxies and Extrasolar systems – how do they obtain it; Fermi Bubbles – two large structures in gamma-rays and X-rays above and below Galactic center; Mysterious Star KIC 8462852 with irregular dimmings; Coronal Heating problem in solar physics – temperature of Sun's corona exceeding that of photosphere by millions of degrees; Cores of Sun and Earth rotating faster than their surfaces; Diversity of Gravitationally-Rounded Objects in Solar system and their Internal Heat; Lightning Initiation problem – electric fields observed inside thunderstorms are not sufficient to initiate sparks; Terrestrial Gamma-Ray Flashes – bursts of high energy X-rays and gamma rays emanating from Earth. Model solves Missing Baryon problem related to the fact that the observed amount of baryonic matter did not match theoretical predictions. WUM reveals Inter-Connectivity of Primary Cosmological Parameters and calculates their values, which are in good agreement with the latest results of their measurements. In 2013, Model predicted the values of the following Cosmological parameters: gravitational, concentration of Intergalactic plasma, relative energy density of protons in the Medium, and the minimum energy of photons, which were experimentally confirmed in 2015 – 2018. The Narrative consists of four Parts: World-Universe Black-Hole Model; 5D World-Universe Model; Hypersphere World-Universe Model; Hypersphere World-Universe Model. New Physics (See Parts I, II, III, and IV on viXra).