In 1986, about 30 years later, the high temperature (High Tc) superconducting (HTS) copper oxides were discovered by Bednorz and Muller [4]. Then extensive studies of neutron scattering on spin dynamics in these novel superconductors revealed that Cu spins strongly fluctuate in the metallic state of hole doped copper oxides [5]. The insulating state of the undoped copper oxides of parent materials of HTS copper oxides, such as La2Cu04, YBa2Cu306 etc. is ascribed to the strong electron correlations, which is defined as the Mott Insulator (Charge Transfer type) [6]. In this case, magnetic structure is rather simple due to the layered structure of oxide perovskites [7] as well as superexchange interaction of neighboring Cu spins in the basal (C) plane. Quantum spin nature associated with strong antiferromagnetic interactions in the C plane plays a characteristic role in these copper oxide compounds, which is considered to be an indispensable ingredient of HTS mechanism [8]. Doping of holes in these antiferromagnetic insulating copper oxides gives rise to the Metal-Insulator (MI) transition and at the same time, induces the novel HTS state in a certain doping concentration range. It is still a big issue whether antiferromagnetic spin fluctuations in the CuC>2 plane persisting in such a novel superconducting state, just mentioned above, is necessary for the HTS mechanism.