As it is known, the Standard Model for particle physics (SM) has been successfully tested at all accelerator facilities and is currently the best tool available for understanding the phenomena on the subatomic scale. Conventional wisdom is that the SM represents only the low-energy limit of a more fundamental theory and that it can be consistently extrapolated to scales many orders of magnitude beyond the energy levels probed by the Large Hadron Collider (LHC). Despite its impressive performance, the SM leaves out a fairly large number of unsolved puzzles. In contrast with the majority of mainstream proposals on how to address these challenges, the approach developed here exploits the idea that space-time dimensionality becomes scale-dependent near or above the low TeV scale. This conjecture has recently received considerable attention in theoretical physics and goes under several designations, from “fractional field theory”, “continuous dimension” to “dimensional flow” and “dimensional reduction”. Drawing from the principles of the Renormalization Group program, our key finding is that the SM represents a self-contained multifractal set. The set is defined on continuous space-time having arbitrarily small deviations from four-dimensions, referred to as a “minimal fractal manifold” (MFM). The book explores the full dynamical implications of the MFM and, staying consistent with experimental data, it offers novel explanations on some of the unsolved puzzles raised by the SM.