Let us define quantum gravity that describes the world beyond the Planck scale. Diffeomorphism invariance is recognized as a gauge invariance [Uti56], together with ordinary gauge invariance for gauge fields including Yang-Mills fields [YM54]. The guiding principles adopted here are diffeomorphism invariance and renormalizability that continuum quantum field theories should have. Performing the path integral over the gravitational field so as to satisfy these principles is the definition of quantization. Moreover, by adding physical requirements such as initial scalar-fluctuation dominance suggested from cosmological observations, we construct a theory of quantum gravity. This theory has a property called background freedom in the high-energy limit, which allows it to overcome the Planck scale wall. In that region, it can be shown that tensor fluctuations, which impede unitarity and the construction of realistic cosmology, are prohibited as unphysical states.