This comprehensive volume introduces a new framework for the next era of computation and machine intelligence. It presents computation as the execution of superoperator systems. Each task is described by a state space, update law, access model, observation rule, resource record, and verification condition. The framework is then applied to major problems in modern computing.Topics include energy efficiency, forrelation, out-of-time-order correlators, Shor-type period finding, HHL-style linear systems, Grover-type search, matrix multiplication, phase estimation, operator geometry, machine learning, runtime systems, and superintelligent compilers.Written for mathematicians, physicists, computer scientists, engineers, artificial-intelligence researchers, technology leaders, and technically trained readers, the book offers a rigorous roadmap toward a new computational paradigm.