In various fields, from particle physics to condensed matter physics, extremely low emittance muon beam is eagerly awaited. We started a new project to realize the extremely low emittance and high intensity muon beam further beyond previous R&D study performed at RIKEN-RAL. To reduce the muon beam emittance, we plan to utilize the room temperature muonium generator, and furthermore, we apply muonium motion-cancellation mechanism using Doppler shift of 1S-2P transition energy. By the cancellation, one can expect the beam emittance better than ΔxΔθx ≈ 100 μm·mrad even at 100 kV extraction field, which can be focused to the size of ~ 1μm by applying electron microscope technique. We are also developing high intensity and extremely stable VUV laser for the muonium ionization, which can efficiently ionize muonium and produce high muon yield of ~ 10 kHz even at RIKEN-RAL (240kW proton with conventional surface muon channel). This new R&D study will open a totally new application to the muon science, namely a Muon Magnetic Microscope (M3). This muon beam enable us to observe sub-μmeter magnetic structure of the condensed matter with the depth resolution less than 10 nano-meter.