This book is devoted to the systematic treatment of nonequi 1 ibrium vibrational kinetics in molecular systems. Particular emphasis is given to the vibrational excitation of diatomic molecules by low-energy electrons in a discharge and by IR photons in laser-pumped systems. The book follows the different steps of the introduction, redistribution, loss, and chemical conversion of the vibrational quanta, from the points of view of the overall kinetics and the dynamics of elementary processes. These two aspects are balanced in a multidisciplinary approach. The different chapters give the basic instruments (theoretical and experimental) which are needed to understand the ki­ netics of nonequilibrium systems. The book will introduce the reader to different areas such as plasmachemistry, laser chemistry, IR and Raman spectroscopy, and relaxation phenomena, emphasizing how the vibrational energy affects such research fields. The chapters dedicated to collisional dynamics involving vibrational excited molecules provide an introduc­ tion to the modern techniques uti 1 ized in the scattering theory of inelastic and reactive collisions. The extension of the vibrational kinetics to polyatomic mole­ cules, discussed in Chap. 10, is the natural bridge between coll ision and coll i­ sionless regimes. In conclusion, we hope that the approach followed in this book will stimulate the collaboration of researchers coming from different research fields, which are too often completely separate.