During the course of far-infrared investigations of inorganic and coordina- tion compounds at Argonne National Laboratory in the years 1962-1966 it became apparent that no suitable book existed which correlated and dis- cussed the important vibrations occurring in this region for these molecules. Early in 1967 the initial steps were taken to write such a book. Then in 1968 an excellent text by Professor David M. Adams entitled Metal-Ligand and Related Vibrations was published. At this point serious consideration was given to discontinuing work on this book. However upon examination of Adams book it became clear that the references covered only the period to 1966. This field of research is accelerating so tremendously and the period 1966-1969 has seen so many new studies that upon reconsideration it was decided to continue writing this text. The references in this book particularly in the last several chapters include many papers published in 1969. However the proliferation of the far-infrared literature has made it impossible to present all the published material that has any bearing on the subject. Many titles do not pertain primarily to the far-infrared region as such and some of this research has been omitted for this reason. Organometallic compounds have been neglected since the author feels that adequate reviews of that subject are available. Other studies may be missing simply because owing to space limitations only the more important researches could be considered. Of course importance may in this case reflect the author s interest and prejudices.