NOVELTY - Producing fatty acids involves: (A) culturing microalgae under conditions that promote high cell density; (B) culturing the microalgae under conditions that promote an increase in cell size and accumulation of fatty acids; and (C) culturing the microalgae under conditions that promote accumulation of fatty acids, where the conditions of each of culturing steps (A), (B) and (C) are different from one another.    USE - For producing fatty acids that are enriched for omega 3 polyunsaturated fatty acids including docosahexaenoic acid (DHA), used in biodiesel production and in biofuel (claimed), in the production of useful chemicals and materials; in the production of products such as lactic acid and propionic acid; in animal feed; as biodiesel fuel; in biodiesel refinery process; as dietary supplement; in drugs and in cosmetics and cleansers. The DHA is used in fetal and infant brain and ocular development, and in the reduction of age-related neurological disorders such as Alzheimer's disease and dementia, and as human food or supplement or nutraceutical.    ADVANTAGE - The process uses multiphase growth conditions that decouple the phases of increasing cell density and increasing cell size and fatty acid production. The method provides improved and efficient high cell density culture method for the production of omega-3 polyunsaturated fatty acids such as DHA. The method produces DHA by mimicking the decoupling of cell division and cell growth/size increase through accumulation of lipids. The method shows higher potential for yields and productivity. The method provides solution to the glut of crude glycerol in that the primary carbon source used in the method is crude glycerol. The use of crude glycerol not only helps to decrease the excess quantity of the substance but also decreases the cost of algal fermentation since it becomes unnecessary to use more purified and thus most costly, feedstock.    DETAILED DESCRIPTION - INDEPENDENT CLAIMS are included for the following:    (1) producing lipids involving: culturing microalgae under conditions that promote cell density of at least 800000 cells per ml of medium; then culturing the microalgae under conditions that promote an increase in cell size and accumulation of lipids; and then culturing the microalgae under conditions that promote accumulation of lipids;    (2) a method for integrating biodiesel production with fatty acid production by microorganisms involving generating biofuel, where the step of generating produces crude glycerol as a byproduct; pre-treating the crude glycerol to form glycerol feedstock; culturing lipid-producing microorganisms using the glycerol feedstock as a carbon source to produce fatty acid-rich algae biomass; processing the fatty acid-rich algae biomass to obtain omega-3 fatty and non-omega-3 fatty acids; separating the omega-3 fatty acids from the non-omega-3 fatty acids; using the non-omega-3 fatty acids in the step of generating the biofuel, where the step of using the non-omega-3 fatty acids in the step of generating the biofuel produces additional crude glycerol, thereby integrating biodiesel production with fatty acid production; and    (3) an integrated biofuel and omega-3 fatty acid production method involving: obtaining biofuel and crude glycerol from a biofuel refining process; using the crude glycerol as a carbon source to produce a fatty acid rich algae biomass containing both omega-3 fatty acids and non-omega-3 fatty acids; collecting the omega-3 fatty acids; and using the non-omega-3 fatty acids to produce biofuel and crude glycerol; and repeating the steps.