Introduction.A wide range of substances can be vitrified by cooling their liquids. At temperatures well below the fusion point, the relaxation time for viscous flow becomes so long that the liquid ultimately behaves like a solid. The glassy states of liquid are found to exhibit the glass transition T g and residual entropy S 0 as indicative of non-ergodicity of the frozen-in non-equilibrium system.1) The liquid undergoes a heat capacity discontinuity over a narrow temperature interval of T g , where the relaxation time for the structural change in a liquid becomes of the order of 1 ks that corresponds to the time scale for a single heat-capacity determination.Corresponding to the C p drop, the entropy of the liquid bends at T g and results in residual entropy S 0 that is a measure of the extent of frozen-in disorder. These quantities are highly time-dependent. If the liquid were cooled with an infinitely slow rate, the liquid follows the extrapolated curve of entropy of the undercooled liquid and finally intersects that of the corresponding crystal. Since any disordered system with less entropy than that of the crystal cannot be considered, the entropy of the equilibrium liquid must bend at this temperature in order to avoid the entropy crisis. The temperature is known as the Kauzmann temperature T K . Thus the seemingly second-order character of the glass transitions in real liquids is believed to be a kinetic manifestation of the underlying second-order phase transition in the "equilibrium" liquid. Essentially the same phenomena were found to occur also in some crystalline solids that have orienta- Abstract: Of prime interest in numerous studies on water, an important substance to all living systems, may be its physical, chemical, biological characteristics in our internal and external environments. One of the central problems underlying all these researches is a basic structural problem. An important question was why ordinary ice did not obey the third law of thermodynamics. The proton-disordered phase I h remains down to the lowest temperature without exhibiting any indication of phase transition. We found that the glass transition is not a characteristic property of liquid but of wide occurrence in condensed systems that failed to maintain thermal equilibrium during continuous cooling. Crystalline substance that exhibited freezing-in process on cooling was designated as "glassy crystals". In fact, ice I h exhibited a glass transition at around 110 K due to slowing down of reorientational motion of the water molecules. A particular kind of impurity was found to accelerate dramatically the motion, and to induce a long-awaited phase transition at 72 K. The transition removed a substantial fraction of the residual entropy of ice. The dopant acted as a kind of catalysis for releasing the immobilized non-equilibrium state to recover thermal equilibrium in the laboratory time. Structure and some properties of the ordered low temperature phase, designated as ice XI, are discussed. The same ordering processes observ...