NOVELTY - Multistage trans-esterification process, with acid catalyst or base catalyst, for the production of biodiesel and glycerin has now been found. Accordingly, one aspect of the present invention provides a multistage process for the trans-esterification of a mixture of triglycerides and fatty acids, comprising: (a) mixing said triglycerides and fatty acids, a low carbon alkyl alcohol, a catalyst, and recycled glycerin and low carbon alkyl alcohol from the second separation device in the first reactor, said low carbon alkyl alcohol been selected from the group consisting of methanol, ethanol, propyl alcohol, and iso-propyl alcohol, or mixtures thereof, and the ratio of said low carbon alkyl alcohol to said triglycerides and fatty acids in said first reactor being in the range of 3:1 to 30:1; and extracting glycerin and low carbon alkyl alcohol from product stream of said first reactor by the first separation device;and partially recycling light product stream to the said first reactor; (b) transporting said light product stream, consists of reactants and products, from said first separation device to the second reactor; mixing said reactants and products, recycled glycerin and low carbon alkyl alcohol from the third separation device, additional low carbon alkyl alcohol and additional catalyst in said second reactor, and the ratio of said additional low carbon alkyl alcohol to said triglycerides and fatty acids being in the range of 0:1 to 9:1; and extracting glycerin and low carbon alkyl alcohol from product stream of said second reactor by the second separation device and transporting said glycerin and low carbon alkyl alcohol to the said first reactor; and partially recycling light product stream to the said second reactor; (c)transporting the light product stream from said second separation device to the third reactor; mixing said light product stream, additional low carbon alkyl alcohol, and additional catalyst in said third reactor, and the ratio of said additional low carbon alkyl alcohol to said triglycerides and fatty acids being in the range of 0:1 to 9:1; and extracting glycerin and low carbon alkyl alcohol from said third reactor by the third separation device and transporting said glycerin and low carbon alkyl alcohol to the said second reactor; and partially recycling light product stream to the said third reactor; (d) separating biodiesel from product stream of said third separation device; (e) processing the glycerin separated from said first separation device to produce crude glycerine; (f) processing the biodiesel separated from said third separation device to produce biodiesel. In the preferred embodiments of the invention, the preferred number of reactors is two or three in series. In the preferred embodiments of the invention, the preferred reactors are continuous stirred tank reactor or tubular plug flow reactor. In the preferred embodiments of the invention, the preferred reaction pressure of said reactors are in the range from 0 bar to 15 bar. In the preferred embodiments of the invention, the preferred reaction temperature of said reactors are in the range from 60 DEG C to 100 DEG C, and lower than the boiling point of said low carbon alkyl alcohol at said preferred reaction pressure. In the preferred embodiments of the invention, the siad catalyst is an acid catalyst or a base catalyst. In the preferred embodiments of the invention, siad acid catalyst is selected from sulfuric acid and anhydrous sulfuric acid. In the preferred embodiments of the invention, said base catalyst is selected from sodium hydroxide and potassium hydroxide.