NOVELTY - Method for cultivating and processing microalgae, involves directing a continuous supply of carbon dioxide into an enclosed photobioreactor containing microalgae, exposing the enclosed photobioreactor to insolation, cultivating, processing to create an algae biomass and a gaseous mixture, separating the algae biomass, extracting the biomass as essentially pure algae oil and oil-free algae biomass, separating the gaseous mixture into unreacted carbon dioxide, recycling the separated unreacted carbon dioxide to the photobioreactor, and storing the oxygen.    USE - The method or system is useful for cultivating and processing microalgae for producing oxygen and algal oil (all claimed) which is used as biodiesel.    ADVANTAGE - The method process oxygen with high purity and is performed with reduced quantity of water.    DETAILED DESCRIPTION - Method for cultivating and processing microalgae, involves directing a continuous supply of carbon dioxide into an enclosed photobioreactor containing microalgae, exposing the enclosed photobioreactor to insolation for the cultivation of the microalgae by controlled photosynthesis chemical reactions, cultivating the microalgae and processing the microalgae to create an algae biomass and a gaseous mixture, separating the algae biomass from the gaseous mixture, extracting the algae biomass as essentially pure algae oil and oil-free algae biomass, separating the gaseous mixture into unreacted carbon dioxide for recycling and oxygen for export, recycling the separated unreacted carbon dioxide to the photobioreactor, and storing the oxygen in synchronization with export. An INDEPENDENT CLAIM is included for system for cultivating and processing microalgae, which comprises unit for directing a continuous supply of carbon dioxide into an enclosed photobioreactor containing microalgae, unit for exposing the enclosed photobioreactor to insolation for the cultivation of the microalgae by controlled photosynthesis chemical reactions, unit for cultivating the microalgae and processing the microalgae to create an algae biomass and a gaseous mixture, unit for separating the algae biomass from the gaseous mixture, unit for separating the algae biomass into essentially pure algae oil and oil free algae biomass, unit for separating the gaseous mixture into unreacted carbon dioxide and oxygen, unit for recycling the separated unreacted carbon dioxide to the photobioreactor, and unit for storing the oxygen.