Characterization represents broad materials’ measurement activities to interrogate their inherent information. Most characterization techniques live one or more spaces including real space (r), reciprocal space (k), energy space (E), and time space (t), commonly called microscopy, diffraction, spectroscopy, and time-domain method, respectively. This graduate-level course aims to offer a holistic, self-contained theoretical foundation of characterization techniques with photons, electron, and neutron probes in various k, E, and t spaces, in order to better elucidate the microscopic interaction mechanisms of materials at a quantum level.