The Theory of Observational Relativity, the theory of OR for short, is a new discovery and a new theory, which has revealed the root and essence of relativity: All relativistic effects or relativistic phenomena are observational effects and apparent phenomena rather than the objective and true physical reality. In particular, the whole theoretical system of OR has generalized and unified Newton’s mechanics and Einstein’s theory of relativity, integrating such two great theories in physics into the identical theoretical system under the identical axiom system. The theory of OR is divided into two parts: the theory of inertially observational relativity (IOR); the theory of gravitationally observational relativity (GOR). The theory of IOR takes the definition of time as the most basic logical premise and theoretically deduces the spacetime transformation of IOR, so-called the general Lorentz transformation, which has generalized and unified the Galilean transformation and the Lorentz transformation. The theory of IOR has proved an important theorem: the invariance of information-wave speeds. It suggests that the invariance of light speed is only a special case of the invariance of information-wave speeds. Actually, Einstein’s invariance of light speed can only be valid when light acts as the observation medium for transmitting observed information to observers. So, the speed of light is not really invariant. Based on the invariance of information-wave speeds, the author has established the whole theoretical system of IOR which has generalized and unified Newton’s inertial mechanics and Einstein’s special relativity, and moreover, integrated de Broglie’s theory of matter waves into the theory of IOR, marching towards the unification of relativity theory and quantum theory. The theory of IOR is logically consistent not only with Einstein’s special relativity but also with Newton’s inertial mechanics. Such logical consistency and strict correspondence show that the theory of IOR is logically self-consistent, and from one aspect, confirm the logical rationality and theoretical validity of the theory of IOR. In particular, the theory of IOR is supported by observations and experiments, including the Michelson-Morley experiment.