This monograph provides a reformulation of relativity theory that emphasizes a direct relationship between the visual observations of observers in relative motion. It draws a clear distinction between actualized observation and inferences from theoretical constructs that cannot be observed. The focus is on visual observations rather than abstractions that have traditionally been supposed to constitute observations in relativity. Penrose and Terrell demonstrated that besides the Lorentz transformation a second 'transformation of the field of vision' is required to transform visual observations between relatively moving observers. The dual transformation set transforms observed circles into circles, refuting Einstein's prediction that spheres would "appear oblate" to an observer in relative motion. In this monograph we proceed further to examine the appearance of wall clocks by applying this same 'transformation of the field of vision'. Using clocks rather than static objects provides a time stamp on a neighborhood of transformed events that accommodates a determination of whether observations are related in accordance with the established interpretation of the Lorentz equations, i. e., does the other observer's clock time appear dilated. We demonstrate an inconsistency with 'frame independence' and 'mutual observability' tenets in this regard. The role of the 'kinematics problem' in Einstein's selection and interpretation of Lorentz transformation equations is discussed as the rationale for his having conjectured Lorentz contraction and time dilation. As points of departure, alternative hypotheses are presented that provide different solutions to this 'problem' with interpretations of the inevitable spatial and temporal disparities which more consistently predict experimental observations. Finally a single transformation with no intermediary metaphysical distractions is derived by embracing observable relativistic aberration and Doppler effects on the electric and magnetic fields of electrodynamics. It provides a physical basis (rather than mere mathematical formalities) for understanding the ostensible effects of relative motion. It supports frame independence and mutual observability and accommodates covariance, generalization, and compatibility with quantum theories