NOVELTY - A heterogeneous catalyst comprises water-insoluble solid(s) and optionally solid substrate.    USE - Catalyst for a transesterification process for producing fatty acid esters or glycerin (claimed).    ADVANTAGE - A conversion of 100% is obtained using prepared catalysts. The purity of the products, such as biodiesel or glycerin, is greater than 96.5%. The catalysts are economically obtained from cheaper raw materials and lower industrial costs of production, making them more attractive for production on a large scale than the catalysts produced by other methods.    DETAILED DESCRIPTION - INDEPENDENT CLAIMS are included for:    (1) a method for producing a solid heterogeneous catalyst comprising barium oxide, including preparing a mixture comprising aluminum oxide and barium oxide octahydrate, optionally the mixture comprises 80% p/p aluminum oxide and 20% p/p of barium oxide octahydrate; peptizing the mixture in an acetic acid solution, optionally where the acetic acid solution is a 4% p/p acetic acid solution; drying the mixture, optionally where the mixture is dried at 120 degrees C, preferably for 8 hours; and heating the mixture, optionally where the mixture is heated at 550 degrees C, preferably for 3 hours;    (2) a method for producing a solid heterogeneous catalyst comprising apatite, including providing apatite; drying the apatite, optionally where the apatite is dried at 120 degrees C for 16 hours; and heating the apatite, optionally the apatite may be heated at 550 degrees C for 3 hours;    (3) a composition which is obtained by a reaction between a vegetable oil or animal fat and an alcohol, where reaction is performed in the presence of a heterogeneous catalyst, and optionally the composition comprises not less than 98% p/p of fatty acid esters and/or not greater than 4500 ppm of fatty acids, and optionally the alcohol is methanol or ethanol; and    (4) a method for producing a composition comprising fatty acid esters, including performing a transesterification reaction between a vegetable oil or an animal fat, and an alcohol using a heterogeneous catalyst, optionally the alcohol is methanol or ethanol.