The main objective of a paper is to discuss the most important Concepts for any Cosmological model: Space, Time, and Gravitation; Cosmological principle (homogeneous and isotropic universe); Universality of physical laws; Law of the conservation of angular momentum; Expansion of universe; Content of the World; Formation of galaxies and large-scale structures; Speed of light in vacuum; Origin of cosmic microwave background radiation. The performed analysis shows that Big Bang Model (BBM) fails to account for these Concepts and should be obsolete. Hypersphere World-Universe Model (WUM) is, in fact, a Paradigm Shift in Cosmology [1]. WUM and BBM are principally different Models: 1) Instead of the Initial Singularity with the infinite energy density and the extremely rapid expansion of the space (Inflation) in BBM; in WUM, there was a Fluctuation (4D Nucleus of the World with an extrapolated radius equals to a basic unit of size a) in the Eternal Universe with a finite extrapolated energy density (four orders of magnitude less than the nuclear density) and a finite expansion of the Nucleus in Its fourth spatial dimension with speed c that is the gravitodynamic constant; 2) Instead of a practically Infinite Homogeneous and Isotropic Universe around the Initial Singularity in BBM; in WUM, the 3D Finite Boundless World (the Hypersphere of the 4D Nucleus) presents a Patchwork Quilt of different Luminous Superclusters ( ≳10^3), which emerged in different places of the World at different Cosmological times. The Medium of the World is Homogeneous and Isotropic. The distribution of Macroobjects in the World is spatially Inhomogeneous and Anisotropic and temporally Non-simultaneous. The Absolute Age of the entire World (determined by the parameters of the Medium) is 14.22 Gyr. The Medium of the World, Dark Matter, and Angular Momentum are the main Three Pillars of WUM.