This book shows how one can combine Yang-Mills gauge symmetry and effective Einstein-Grossmann metric tensors to tackle physical problems at microscopic, macroscopic and super-macroscopic length scales. In particular, the combination of gauge symmetry and an effective metric tensor provides a framework for and leads to an alternative dynamics of cosmic expansion based on quantum Yang-Mills gravity at the super-macroscopic limit. Together with the cosmological principle, one can investigate and derive expanding scale factors, the age of the universe, the cosmic redshift, and the Hubble recession velocity. Furthermore, this framework leads to a possible explanation for the late-time accelerated cosmic expansion due to baryon masses and charges. All these discussions are based on the operationally defined space and time coordinates of inertial frames. Finally, this book expounds on the intimate relationship between space-time translation gauge symmetry and the beautiful ideas of the Lie derivative and Pauli's variation. One interesting application of the Lie derivative is to formulate a gravitational theory with an external space-time gauge group, which leads to Yang-Mills gravity.