The book introduces the Field Theory of Nonimaging Optics as a new analytical paradigm, not statistical, to analyze problems in the frame of nonimaging geometrical optics, with a formulation based on field theory of irradiance vector . This new paradigm provides new principles and tools in the optical system design methods, complementary to flowline method, overcoming the classical ray paradigm. This new Field paradigm can be considered as a generalization of the ray paradigm and new accurate and faster computation algorithms will be developed. In a parallel way, the advance in the knowledge of the principles of Field Theory of Nonimaging Optics has produced clear advances in the connection between nonimaging optics and other apparently disconnected theories of radiation transfer. The irradiance vector can be considered as the macroscopic average of Poynting vector, with a clear connection with radiation pressure. Lorentz geometry techniques can also be applied to study irradiance vector . There are clear thermodynamic connections between the nonimaging concentrator and Stefan-Boltzmann law of radiation. From this thermodynamic connection, nonimaging optics and irradiance vector can also be studied from a phase space point of view. This book is intended for researchers, graduate students, academics and professionals looking to analyze, design and optimize optical systems.