This book examines the nature of the coherent excitation produced in atoms by lasers, as well as the details of the transient variation of excited-state populations with time and how these depend upon such controllable parameters as laser frequency and intensity. It emphasizes the physical and mathematical theory that underlies contemporary description of this excitation. It is concerned with temporal behaviour rather than with the characteristic energy levels of the stationary status of atoms. In Volume 2, Part IV a variety of multi-state extensions of the simple two-state atom, beginning with three- state models and continuing to finite and infinite chains of excitation are examined. Part V presents and applies the theory of angular momentum to coherent excitation. The final part examines a number of extensions of coherent excitation, concluding with the theory of random processes and applications to the fluctuations that inevitably accompany excitation and act to destroy coherence. A set of appendices summarize background material.