In this work, we present a new Cosmology of the Grand Universe, which is a relativistic model of the steady-state, matter-antimatter symmetric Universe in infinite space-time. The Grand Universe consists of matter and antimatter bounded Universes, which are floating in an infinite space filled with the physical Grand Universe Background. The Grand Universe methodology is based on Fundamental Principles of Classical Mechanics and Special Relativity Dynamics, and it explains all basic cosmological observations consistently with Fundamental Principles of Physics. Issues of relationships of cosmological models with Relativistic Gravitation theories and Modern Physics branches are discussed. A detailed critical analysis of the Standard Cosmological Model is conducted, especially, in part of its methodological basis, the metric of space expansion as the solution of GR field equations. The attention is paid to the damaging role of abstract mathematical constructions in Physical theories. The issues related to philosophical criteria of true versus false in Cosmology and Modern Physics, in general, are discussed as well. The conclusion is made that the Standard Cosmological Model suffers numerous inner contradictions due unproven assumptions and the corresponding conflicts with observations, so it must be abandoned in favor of the Grand Universe Model.