NOVELTY - Separating (M1) neutral lipids from intact algal cells involves: providing a wet algal biomass comprising intact algal cells which comprise proteins that are soluble in a mixture of an amphipathic solvent and water, polar lipids and neutral lipids; dewatering the wet algal biomass; mixing the partially dewatered wet algal biomass with first amphipathic solvent set, and first hydrophobic solvent set to generate a first extraction mixture comprising a first heavier phase and a first lighter phase; separating, mixing, recycling and again separating step.    USE - For separating neutral lipids from intact algal cells (claimed); for generating renewable fuels as well as food products and supplements; for extracting and fractionating algal products e.g. oils and proteins, algal oil, algal proteins, and algal carotenoids.    ADVANTAGE - The method provides efficient separation of algal neutral lipids from wet algal biomass while avoiding emulsification of extraction mixtures; is improved by introducing a highly non-polar solvent to extraction system, thus avoiding cost of evaporating and recycling all of solvent used for extraction; provides ability to accomplish preliminary refining, because the hydrophobic solvent in the system selectively separates the products further into lipids and non-lipid components; enables recovery of significant portion of the valuable components, including polar lipids, in the algae. The obtained neutral lipid fraction possesses a low metal content, thus enhances stability of lipid fraction, and reduces subsequent processing steps. The method allows extraction of metals in protein or polar lipid fractions. This is advantageous because proteins and polar lipids are not highly affected by metal exposure, and in some cases are actually stabilized by metals.    DETAILED DESCRIPTION - Separating (M1) neutral lipids from intact algal cells involves: i) providing a wet algal biomass comprising intact algal cells which comprise proteins that are soluble in a mixture of an amphipathic solvent and water, polar lipids and neutral lipids; ii) dewatering the wet algal biomass by removing extracellular water to increase the solid content of the wet algal biomass to 5-50 wt.% to generate a partially dewatered wet algal biomass; iii) mixing the partially dewatered wet algal biomass with a first amphipathic solvent set in a ratio of one part first amphipathic solvent set to one part wet algal biomass by weight, and a first hydrophobic solvent set to generate a first extraction mixture comprising a first heavier phase and a first lighter phase, where the first heavier phase comprises the first amphipathic solvent set, neutral lipids, proteins that are soluble in a mixture of an amphipathic solvent and water, and partially dewatered wet algal biomass and the first lighter phase comprises the first hydrophobic solvent set and polar lipids; iv) separating the first lighter phase of the extraction mixture from the first heavier phase of the extraction mixture; v) separating the partially dewatered wet algal biomass from the first amphipathic solvent set in the first heavier phase of the extraction mixture to generate a separated partially dewatered wet algal biomass comprising neutral lipids; and a protein mixture comprising proteins that are soluble in a mixture of an amphipathic solvent and water, water and the first amphipathic solvent set; vi) mixing the separated partially dewatered algal biomass with a second amphipathic solvent set in a ratio of one part second amphipathic solvent set to one part separated partially dewatered wet algal biomass by weight, and a second hydrophobic solvent set to generate a second extraction mixture comprising a second heavier phase and a second lighter phase, where the second heavier phase comprises the second amphipathic solvent set and separated partially dewatered wet algal biomass and the second lighter phase comprises the second hydrophobic solvent set and the neutral lipids; viii) separating the second heavier phase from the second lighter phase; viii) recycling at least a portion of the second heavier phase for further mixing with a third amphipathic solvent set in a ratio of about one part third amphipathic solvent set to one part separated partially dewatered wet algal biomass by weight, and a third hydrophobic solvent set to generate a third extraction mixture comprising a third heavier phase and a third lighter phase, where the third heavier phase comprises the third amphipathic solvent set and separated partially dewatered wet algal biomass and the third lighter phase comprises the third hydrophobic solvent set and the neutral lipids; ix) separating the third heavier phase from the third lighter phase; and x) separating the neutral lipids from the second lighter phase and the third lighter phase, where the first lighter phase has a higher concentration of polar lipids than the second and third lighter phases, and the second and third lighter phases have a higher concentration of neutral lipids than the first lighter phase. An INDEPENDENT CLAIM is included for separating (M2) neutral lipids from intact algal cells involving: the step i); mixing the wet algal biomass with a first amphipathic solvent set in a ratio of one part first amphipathic solvent set to one part wet algal biomass by weight, and a first hydrophobic solvent set to generate a first extraction mixture comprising a first heavier phase and a first lighter phase, where the first heavier phase comprises the first amphipathic solvent set, neutral lipids, proteins that are soluble in a mixture of an amphipathic solvent and water, and wet algal biomass and the first lighter phase comprises the first hydrophobic solvent set and the polar lipids; the step iv); separating the wet algal biomass from the first heavier phase of the extraction mixture to generate a separated wet algal biomass comprising neutral lipids; and a protein mixture comprising proteins that are soluble in a mixture of an amphipathic solvent and water, water and the first amphipathic solvent set; mixing the separated algal biomass with a second amphipathic solvent set and a second hydrophobic solvent set in a ratio of one part amphipathic solvent set to one part separated wet algal biomass to generate a second extraction mixture comprising a second heavier phase and a second lighter phase, where the second heavier phase comprises the second amphipathic solvent set and separated wet algal biomass and the second lighter phase comprises the second hydrophobic solvent set and the neutral lipids; the step vii); the step viii); and separating the neutral lipids from second lighter phase and third lighter phase to generate a neutral lipids fraction, where first lighter phase has higher concentration of polar lipids than second and third lighter phases, and second and third lighter phases have higher concentration of neutral lipids than first lighter phase.