Semiclassical mechanics relates Newton's classical theory to modern quantum mechanics in a manner designed for the interpretation of the most recent experimental evidence. The theory is physically intuitive and computationally accurate, and is particularly powerful for large quantum numbers - hence it has special reference to atomic, nuclear, and molecular physics. It also proves to be remarkably accurate even for the lowest quantum states. This book gives a comprehensive account of the application of the theory to molecular systems, with particular attention paid to the problems of non-separability. Spectroscopy is addressed in addition to collision theory. Although it is primarily a research monograph, the inclusion of problems at the end of each chapter makes this book equally applicable as a graduate text.