As the name suggests, the 'dark matter' does not interact with the 'luminous matter' through interactions different from gravity, or it possibly couples weakly with the other cosmic components. The high dark matter content of the Universe reveals its existence across different 'space time' scales by perturbing the kinematical and dynamical properties of galaxies, and clusters of galaxies, lensing the cosmic background radiations, driving the cosmological evolution phases, clustering the visible matter in small and large-scale structures.Nobody currently knows the real nature and microscopic properties of this dark and macroscopic constituent of the Universe. Coherently approaching the fundamental questions, this book critically explores the role of the 'space time' by fixing the representations of its underlying symmetries and classifying the relevant scattering portals of the principal dark matter candidates. With particular reference to the experimental constraints on annihilation and direct detection cross sections, the author in a consistent way reviews the kinetic and thermodynamic evolution since the decoupling era of what would have become the dark matter relics at the cosmological scale and the dark halos at the galactic scale, clarifying the distinction between the -- mixed or pure -- cold, warm and hot dark matter cosmological models.The two last chapters discuss the methodologies which subtend and support the experimental approaches to determine the constraints on the macroscopic and microscopic dark matter properties.In good synthesis, the ultimate scope of the book is to present the logic interplay between the microscopic and the macroscopic points of view on the 'dark matter problem', by finding their unifying key element in the intimate nature of the 'space time'.