This treatise presents a new scientific theory of the nature of consciousness and its relation to the brain. It is based on a comprehensive review of neuroscience, cognitive science, introspectionist psychology, clinical neurology, philosophy and the cosmology of space and time. The theory was adumbrated by More, Priestly, Borad, Price and Russell. It links these philosophical suggestions with recent developments in physics - Kaluza's theory of electromagnetism and Linde's theory of consciousness. Topics covered include scientific and philosophical aspects of perception, contrasting the Representative Theory with Direct Realism; the body-image of neurology; the binding problems in neuroscience; theories of mind/brain relation; and how the brain mechanisms that are involved in generating phenomenal consciousness actually work. The basic concept deals with the geometrical and topological relations between phenomenal space and physical space using higher-dimensional geometry and tensor field theory. Experiments to test the theory are suggested.