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LED technology is a multidisciplinary subject that involves semiconductor physics, photometry, electric power, heat, and chromaticity. It has been demonstrated that operating the LED load at its rated power does not necessarily guarantee optimal luminous performance unless the LED system is properly designed. This paper presents a tutorial of LED system theory that links the device characteristics to optimal system designs. Based on recent works on the photoelectrothermal theory and its extensions, this paper aims at providing a comprehensive LED system theory with physical explanations for electronics engineers and researchers working in LED system designs, with the emphasis on general and public lighting applications. The physical meanings of essential parameters are explained. Practical test procedures for extracting parameters not readily available in data sheets are included. It is envisaged that this LED system theory will form the basic design guidelines for future LED system designs. This tutorial paper is written not only for educational purpose, but it also highlights important parameters that LED device manufacturers should include in LED data sheets.