NOVELTY - Removing products from an algal biomass, comprises: e.g. combining an algal biomass and a first solvent set, to generate a first extraction mixture; separating at least a portion of the first liquid phase of the first extraction mixture from the first substantially solid phase; combining the first extraction substantially solid phase and a second solvent set, to generate a second extraction mixture; and separating at least a portion of the second liquid phase of the second extraction mixture from the second substantially solid phase.    USE - The method is useful for removing products from an algal biomass comprising substantially intact algal cells (claimed), where the product is useful for the production of renewable fuels and nutritional products, and the algal product is algal oil, algal proteins, and algal carotenoids.    ADVANTAGE - The method is highly selective and provides high yield of algal products in an economical manner.    DETAILED DESCRIPTION - Removing products from an algal biomass comprising substantially intact algal cells, comprises: combining an algal biomass and a first solvent set, to generate a first extraction mixture, where the first extraction mixture includes a first substantially solid phase and a first liquid phase; separating at least a portion of the first liquid phase of the first extraction mixture from the first substantially solid phase; combining the first extraction substantially solid phase and a second solvent set, to generate a second extraction mixture, where the second extraction mixture includes a second substantially solid phase and a second liquid phase, and the second extraction mixture is less polar than the first extraction mixture; separating at least a portion of the second liquid phase of the second extraction mixture from the second substantially solid phase; combining the second extraction substantially solid phase and a third solvent set, to generate a third extraction mixture, where the third extraction mixture includes a third substantially solid phase and a third liquid phase, and the third extraction mixture is less polar than the second extraction mixture; and separating at least a portion of the third liquid phase of the third extraction mixture from the third substantially solid phase.