This book highlights the author’s works in the past 20 years. The main idea is that molecular highly-excited vibration is a nonlinear, many-body and semiclassical system. Therefore, many ideas and techniques in nonlinear fields such as chaos, resonance, Lyapunov exponent, etc. can find their places in this study. Together with the Lie algebraic coset algorithm, readers are able to approach the topics in a simple arithmetic and realistic way in contrast with the traditional solving of Schrö dinger equation. These works bridge the gaps between molecular vibration and nonlinear sciences. Readers can understand and find many new characters for molecular highly-excited vibration from a fresh viewpoint of nonlinearity, especially, the chaos. Related works of the elementary ideas in this field are first quoted in the first three chapters for the readers to be familiar with. The rest of the chapters offer concrete examples by this approach with flourishing ideas and results about system dynamics which are not known or neglected by the traditional wave function algorithm. Key Features: ○It broadens the prospects of molecular vibration to high excitation ○It broadens the treatment of molecular vibration to algebraic and nonlinear methods