The main objective of a paper is to discuss the most important Concepts for any Cosmological model: universality of physical laws; cosmological principle (homogeneous and isotropic universe); Space, Time, and Gravitation; speed of light in vacuum; structure and content of the World; dark matter and ordinary matter; origin of matter (singularity or continuous creation); Law of Conservation of Angular Momentum; Primary Cosmological Parameters; Four Pillars of Standard Cosmology (SC) – expansion of Universe, nucleosynthesis of light elements, formation of large-scale structures, origin of cosmic background radiation. The performed analysis shows that SC fails to account for most of these concepts. The most intriguing result is that there was no Initial Singularity: all galaxies are gravitationally bound with their Superclusters. Proposed Hypersphere World-Universe Model (WUM) is, in fact, a Paradigm Shift in Cosmology. According to WUM, Superclusters are, in fact, the principal objects of the World. Macroobjects form from the top (Superclusters) down to galaxies and extrasolar systems in parallel around different Cores made up of different Dark Matter Particles. Formation of galaxies and stars is not a process that concluded ages ago; instead, it is ongoing.