NOVELTY - Producing fatty acid alkyl ester and/or glycerin involves a first reaction step of reacting fat and oil with alcohol over a solid catalyst; a first alcohol stripping step of evaporating, from a first reaction liquid obtained in the first reaction step, unreacted alcohol that remains without reacting in the first reaction step; and an alcohol refining step of refining the alcohol from the unreacted alcohol with use of at least a part of heat of the unreacted alcohol.    USE - For producing fatty acid alkyl ester and/or glycerin (claimed). The fatty acid alkyl ester is useful for e.g. biodiesel fuel, foods, cosmetics, medicines, fuels; and glycerin is useful for making e.g. nitroglycerin, raw materials for resin, medicines, foods, paints, and cosmetics.    ADVANTAGE - The method produces high-quality fatty acid alkyl ester and/or glycerin with high yield and easiness by using heat of unreacted alcohol evaporated from a reaction liquid obtained through transesterification as energy necessary for purifying alcohol from the unreacted alcohol; reduces production cost in producing fatty acid alkyl ester and glycerin over a solid catalyst i.e. reduces energy cost for reusing unreacted alcohol in producing fatty acid alkyl ester and glycerin. The use of evaporator including a heat exchanger with a short residence time increases the yield and purity of fatty acid alkyl ester. Evaporation of alcohol in a glycerin phase that is obtained in the first phase-separation step simultaneously with the evaporation of unreacted alcohol increases the purity of glycerin. Evaporating alcohol before the second phase-separation step reduces distribution of fatty acid alkyl ester to glycerin phase, and increases yield of fatty acid alkyl ester. The method suppresses drop in activity of solid catalyst, i.e. lengthening the life of solid catalyst. When the life of solid catalyst is lengthened, frequency of catalyst exchange is decreased, and labor required for catalyst exchange can be reduced. Thus increases the amount of fatty acid alkyl ester and/or glycerin produced with respect to the same amount of solid catalyst, and reduces costs for solid catalyst with respect to each product. The suppressing of the drop of activity of solid catalyst reduces frequency of troublesome exchanging of a solid catalyst with dropped activity in producing fatty acid alkyl ester and/or glycerin. The energy required in the alcohol refining step can be obtained from heat generated inside the reaction system. Thus reduces the amount of energy to be produced outside the reaction system. This reduces cost for producing fatty acid alkyl ester and glycerin over a solid catalyst. With the arrangement, in the third alcohol stripping step, the alcohol is evaporated with use of evaporator including the heat exchanger with a short residence time. Consequently, excessive heating of fatty acid alkyl ester and/or glycerin is prevented and thus preventing reverse reaction from proceeding. The method omits refining after the phase-separation. The device shows higher operation efficiency. The method produces fatty acid alkyl ester and glycerin cheaply, industrially, and environment-friendly.    DETAILED DESCRIPTION - An INDEPENDENT CLAIM is included for a device for producing fatty acid alkyl ester and/or glycerin comprising a reactor for reacting fat and oil with alcohol over a solid catalyst; a stripper for stripping, from a reaction liquid obtained in the reactor, unreacted alcohol that remains without reacting in the reactor; and a refiner for refining the alcohol from the unreacted alcohol stripped in the stripper, with use of at least a part of heat of the unreacted alcohol.