The method of observing the response of a solid to an applied mechanical vibration - mechanical vibration method - is useful for investigating various physical properties of materials. Topics used include the characterization of defects in crystals, nonlinear elasticity of crystals, electron conduction and superconductivity, and melting phenomenon. The materials are inorganic, organic, and metallic glasses of various kinds. The phenomena of the glass transition and crystallization are the main objects. Viscosity, internal friction, ultrasound propagation, and Brillouin scattering experiments are used. This book presents research in order to show the utility of the method by examining the formalism of the elasticity and mechanical vibration, as well as research concerning crystalline solids.