According to Einstein, the fundamental laws of physics must be symmetric or ‘manifestly covariant’ – that is - remain the same in mathematical form under symmetry transformations. As such, it is impossible to distinguish an absolute observer/preferred frame (is the train moving or is it you moving away from the train). It is not at all obvious that a mathematical enforcement of this symmetry theme leads to the most fundamental (and successful) physical theories known; the Standard Model (SM) and Special and General relativity (SR & GR). The mathematical framework for symmetry in Physics is Group Theory. This talk builds on the familiarity and symmetry of ordinary space, SO(3), and creates a path to the physical laws of space-time, SO(1,3), and SR (plus predictions, E=mc^2) with a hint of GR. Additional internal, SU(3)XSU(2)XU(1), symmetries applied to space-time, in turn, lead to all the known particles and interactions of the SM – all from symmetry and, ok, a couple of additional nifty tricks. I will use the ideas of symmetry and physics to venture into the Group theory as best I can (with your assistance) to help bridge the connections between Fundamental Physics and Group Theory and some of us in math and physics.