This paper presents a novel theoretical paradigm — Scale-Dependent Geometrodynamics (SDG), offering a conceptually different approach to understanding the fundamental structure of reality. Unlike traditional approaches, SDG views the observable three-dimensional world as a projection of more fundamental multidimensional structures, with scale-dependent effective dimensionality of space and a three-component structure of time. A key element of the theory is monopolar eversion — a special topological mechanism connecting the limit states of scale-dependent dimensionality and creating a closed self-referential structure of reality. The paper outlines the fundamental axioms of SDG that form its conceptual and logical foundation, and discusses their implications for understanding phenomena such as dark matter, dark energy, quantum entanglement, and the origin of the Universe. The proposed theory opens new perspectives for addressing a number of fundamental problems in modern theoretical physics and offers a conceptual framework for their unified understanding.