Rotation plays an essential role in the structure and variation of large-scale flows taking place in the interiors, atmospheres and oceans of planets. Knowledge of common hydrodynamical processes in rotating systems constitutes a major necessary component not only in oceanography, but also in planetary and astrophysical sciences. There have been few systematic accounts of the theory of rotating fluids in the more than quarter of a century since Chandrasekhar (1961) and Greenspan (1968) wrote their classic monographs. The second edition of Greenspan's book, Greenspan (1990), was not a major revision. Other volumes, such as the book edited by Roberts and Soward (1978), while containing some interesting articles, did not present the subject in a unified fashion. More recent books by Vanyo (1993) and Boubnov and Golitsyn (1995) mainly concentrate on experimental studies of general rotating flows. Many important developments have taken place in the study of rotating fluids and it has long been necessary to fill a significant gap in the existing literature.

Over the past several decades the subject of rotating fluids has blossomed remarkably and great strides have been made in our understanding of the topic. Not only have there been very many publications on the classic applications of the theory of rotating fluids to the dynamics of atmosphere and oceans, almost exclusively dealing with thin, nearly two dimensional spherical layers of fluids or infinitely unbounded fluid layers, but also considerable attention has been paid to rotating flows in fluid-filled containers such as cylinders, annuli and thick spherical layers or in complete spheres of fluid. Such studies are often considered to be relevant to the dynamics of planetary and stellar interiors and, more importantly, corresponding laboratory experiments in these fluid-filled rotating containers can be carried out, offering deep insight into the understanding of common processes at the heart of rotating flow phenomena.

It is clearly quite impossible today to cover the theory of rotating fluids to the same degree of completeness as Chandrasekhar (1961) or Greenspan (1968) could for the state of the subject in the 1960s.