This book presents an original theory, based on more than a decade of research, of the behavior of strongly interacting particles in high-energy collision processes. Using gauge field theories, the authors systematically study elastic as well as multiparticle production processes and diffractive scattering, arriving at the conclusion that the total cross section should rise, that is, the particles should "expand," as energies increase. Cheng and Wu compare their results with experimental data, including the outcomes of a series of experiments conducted in the mid-1970s that dramatically confirmed their predictions of rising total cross section at high energies and the dependence of cross sections on the momenta of incoming and outgoing particles. The presentation is systematic and mathematically rigorous yet broad enough to be accessible to graduate students. After a clear presentation of the basic elements of particle physics as well as the quantum theory of gauge fields, the authors take up fermion-fermion elastic scattering, high-energy scattering models, multiparticle production, elastic amplitude, the rising total cross section, phenomenology, the scattering of particles with a structure, the method of calculation by means of momentum variables, tower diagrams, quarkquark scattering in non-Abelian gauge field theories, and multiparticle unitarity and the eikonal formula. included in the appendixes is a detailed discussion of the Feynman parameter method, the power of which is fully illustrated by examples drawn from the authors" experiences. Hung Cheng is Professor of Applied Mathematics at MIT. Tai Tsun Wu is Cordon McKay Professor of Applied Physics at Harvard University.