We propose the Alternative Cosmology, the Grand Universe Model. Here, its Physical Principles and a methodology based on Special Relativity Dynamics of gravitating matter and its Newtonian limit are presented. This is a model of the steady-state, matter-antimatter symmetric Universe in infinite space-time. The Universe is self-sustained in a process of matter-antimatter annihilation and recreation. The Model explains all basic observations. Longstanding and newly appearing problems of the Standard Cosmological Model on small and large observational scales do not arise there.