Revolutionary and original, this treatise presents a new paradigm of EMERGENCE and COMPLEXITY, with applications drawn from numerous disciplines, including artificial life, biology, chemistry, computation, physics, image processing, information science, etc.CNN is an acronym for Cellular Neural Networks when used in the context of brain science, or Cellular Nonlinear Networks, when used in the context of emergence and complexity. A CNN is modeled by cells and interactions: cells are defined as dynamical systems and interactions are defined via coupling laws. The CNN paradigm is a universal Turing machine and includes cellular automata and lattice dynamical systems as special cases.While the CNN paradigm is an example of REDUCTIONISM par excellence, the true origin of emergence and complexity is traced to a much deeper new concept called local activity. The numerous complex phenomena unified under this mathematically precise principle include self organization, dissipative structures, synergetics, order from disorder, far-from-thermodynamic equilibrium, collective behaviors, edge of chaos, etc.Written with a high level of exposition, this completely self-contained monograph is profusely illustrated with over 200 stunning color illustrations of emergent phenomena.