NOVELTY - Producing biodiesel (B1) from feedstock involves: (i) pretreatment step: by subjecting feedstock to filtration to remove solid particles upto 2 microns, and distilling to obtain final distillate; (ii) esterification by contacting final distillate with methanol in presence of immobilized solid heterogeneous esterification catalyst, to form biodiesel, methanol, water and optionally free fatty acid (FFA); and/or (iii) transesterification of esterification product with methanol in presence of immobilized solid heterogeneous transesterification catalyst to form (B1) and glycerin.    USE - For producing biodiesel from feedstock (preferably edible oil, inedible oils, fats, greases brown grease, traps grease, used cooking oil, used cooking fat, animal fat, animal grease, fatty acid distillate, tallow, pork fat, poultry fat, lard, choice white grease, algae oil, crude vegetable oils, soybean oil, corn oil, coffee oil, hemp oil, linseed oil, rice bran oil, jojoba oil, tall oil, mustard oil, distillers grain oil (dried distillers grains (DDG) corn oil), Jatropha oil, camelina oil, rapeseed oil, canola oil, Moringa oil, Pongamia oil, sunflower oil, safflower oil, crude palm oil, palm kernel oil, palm fatty acid distillate, palm sludge oil, coconut oil, elevated levels of at least one of water, sulfur, phosphorus, gums/lipids, sterols, calcium, magnesium, iron, copper, cobalt, manganese, nickel, sodium, potassium, chlorophyll, carotenoids, xanthophylls, proteins and carbohydrates, aldehydes, ketones, carboxylic acids, perchloroethylene, polyaromatic hydrocarbons, polychlorinated hydrocarbons, polymerized triglycerides, pesticides, soaps, detergents, sulfonates, sulfates, phosphatides, phytosterols, sitosterols, cholesterol, and sterol glucosides) (all claimed).    ADVANTAGE - The present method does not provides the generation of toxic waste, that would otherwise be disposed of e.g. in a land-fill; produces biodiesel with high yield (preferably above 99.5 wt.%) and high purity (preferably at least 99 wt.%); uses relatively wide-variety of inexpensive and low-grade feedstock (such as brown grease, trap grease, and high free fatty acid based grease used cooking oil and animal fats, such as tallow, pork fat, poultry fat, lard, and choice white grease), that would otherwise be considered waste and disposed of e.g. in a land-fill; has relatively low energy consumption; and also provides production of commercial or industrial amounts of biodiesel and/or glycerin (e.g. 1000 gallons) in a relatively short period of time (e.g. within about 48 hours). In the present method, the esterification employs a solid, heterogeneous esterification catalyst as a result the process produces little or no soap. As such, any subsequent glycerin separation becomes relatively easier (in the absence of soaps and salts). Traditional transesterification technologies sometimes employ sodium methylate, which leads to saponification issues, which in turn affects biodiesel-glycerin separation and lowers the glycerin purity, leading to a higher acid number and yield loss. Use of acids to neutralize and split he soaps typically leads to higher operating cost and disposal issues. Slower kinetics leads to larger footprint and restricts the use feedstocks higher in FFA, which are typically significantly less expensive than virgin oils. But, the present method employ a solid, heterogeneous transesterification catalyst, as a result the transesterification can be carried out at lower temperatures (e.g. 95 degrees F), the elimination of (or the ability to avoid the use of) sodium methylate, relatively short conversion times (e.g. 30-45 minutes retention time at each reactor stage), relatively high yields (e.g. above 99 wt. % conversion of triglycerides to biodiesel and glycerin), relatively high purity (preferably above 95 wt.%).    DETAILED DESCRIPTION - Producing biodiesel from feedstock involves: (a) filtering a biodiesel feedstock, thereby separating from the feedstock solid particles having a diameter up to 2 microns, to provide a filtrate and a retentate; (b) separating water from the filtrate, to provide a dried filtrate; (c) distilling the dried filtrate, to provide a distillate and a residue; (d) distilling the distillate to provide a subsequent distillate and optionally a subsequent residue; (e) repeating at least one of steps (c) and (d), at least one time, by distilling the subsequent distillate, to obtain a final distillate; (f) passing the final distillate through an ion exchange resin; (g) contacting (i) methanol, (ii) a solid heterogeneous esterification catalyst immobilized on a solid support, and (iii) the final distillate, where the contacting is carried out under conditions to provide an esterification reaction product comprising biodiesel, methanol, water, and optionally free fatty acids; (h) separating water and methanol from the esterification reaction product; (i) contacting the esterification reaction product with (i) methanol and (ii) a solid heterogeneous esterification catalyst immobilized on a solid support, where the contacting is carried out under conditions suitable to provide a subsequent esterification reaction product comprising biodiesel, methanol, water and optionally free fatty acids, where the methanol separated from the esterification reaction products is purified to a purity of at least 99.9 wt.%, and is employed in a subsequent esterification and/or transesterification; (j) contacting at a temperature of less than 102 degrees F (38.89 degrees C) (i) methanol, (ii) a solid heterogeneous transesterification catalyst immobilized on a solid support, and (iii) the esterification reaction product, where the contacting is carried out under conditions suitable to provide a biodiesel, methanol, water, glycerin and optionally triglycerides; (k) separating water, glycerin and methanol from the transesterification reaction product; (l) contacting the transesterification reaction product with (i) methanol and (ii) a solid heterogeneous transesterification catalyst immobilized on a solid support, where the contacting is carried out under conditions suitable to provide a subsequent transesterification reaction product comprising biodiesel, methanol, water, glycerin and optionally triglycerides; and where the methanol separated from the transesterification reaction products is purified to a purity of at least 99.9 wt.%, and is employed in a subsequent esterification and/or transesterification; (m) removing glycerin, water and methanol from the transesterification reaction products, to provide a mixture comprising biodiesel; (n) distilling the methanol obtained from the transesterification reaction products, at least one time, to provide methanol having a purity of at least 99 wt.%, and reusing the purified methanol in a subsequent esterification and/or transesterification; and (o) distilling the biodiesel at least one time, to provide a purified biodiesel.