This book shows how to derive the simple and accurate semiclassical methods analytically and its applications to excited-state molecular dynamics and spectroscopy simulation with and without classical trajectories. It consists of eight chapters demonstrating interesting conical and intersystem-driven phohemical processes in complex systems targeting on large-scale ab initio direct nonadiabatic molecular dynamics. It also includes two chapters dealing with time-independent and time-dependent nonadiabatic molecular dynamics and clarifies the underline principle of Born-Oppenheimer approximation associated with coherence/decoherence quantum effects that have a wide range of applications in phohemistry and photophysics. This book is interesting and useful to a wide readership in the various fields of basic quantum chemistry and physics associated with large-scale excited-state simulation of nonadiabatic molecular dynamics and spectroscopy.