Diffeomorphism invariance, together with gauge invariance for gauge fields, is believed to be a fundamental principle that holds true from classical theory to quantum theory, and from the infinitesimal scale to the cosmic scale. Although it is often pointed out that gravity is incompatible with quantum theory, they are never contradictory. However, we need to be careful about some differences from normal quantization in which Hamiltonian eigenstates are considered. The most important differences is what is commonly called the Hamiltonian and momentum constraintsHamiltonian/momentum constraints, which states that the Hamiltonian and momentum of the whole system vanish. When considering quantum gravity, we should pay more attention to their existence. The background freedom is an ultimate form shown under the constraints. Here, we briefly summarize the physical meaning of them before describing dynamics of quantum gravity in later chapters.