In this book a new method of nonperturbative quantum field theory is developed which offers an alternative version of the common treatment of these problems, and which, in addition, is adapted to the investigation of composite particle dynamics and reactions, or, synonymously, to the investigation of the structure of matter. This new method is based on the Algebraic Schrodinger Representation of canonically quantized (relativistic) fields, and the derivation, formulation and application of this representation will be extensively discussed in Chapters 3, 4 and 5. In this method use is made of the Hamiltonian formalism in combination with elements of the algebraic representation theory of quantum fields and Heisenberg's equation of motion.