This monograph is the outgrowth of a set of notes that were prepared some years ago for a course that in fact never was taught. The notes lay fallow until the occasion of my 75th birthday, which inspired me to try to clean up my computer files. Upon discovering these notes, I consulted David Furbish regarding using these as the basis of a monograph on geophysical waves and flows. His encouraging response gave me the confidence to attempt to do so. This is the outcome of that endeavor.

The goal of that course was – and of the current monograph is – to present a unified approach to geophysical waves and flows, starting from the simplest case and progressively adding complicating factors in a systematic manner. Simplest are sound waves that occur in air and water. Similar, but somewhat more complicated, are compressive body waves (P waves), transverse waves (S waves) and edge waves (Rayleigh and Love waves) in Earth's mantle. Seemingly similar, but dynamically distinct, is the fluid edge wave (think of ocean waves), occurring in both deep and shallow water. It is a short step from shallow-water waves to flows in a horizontal channel. Next, if the channel is sloping, we encounter gravitationally driven flow and this leads naturally to the study of turbulent flows. These topics are found in Chapters 9–13 and 19–23 of this monograph.

In order to approach the analysis of waves and flows properly with a sound theoretical basis, we need to begin from square one, quantifying the manner in which a continuous body can move (kinematics), the nature of the forces that make it do so (dynamics) and the form of its response (rheology). These essential topics are covered in Chapters 3–7. Of course, rotation of Earth affects many types of waves and flows, so this subject is introduced in Chapter 8, with waves affected by rotation investigated in Chapters 15–18 and flows affected by rotation investigated in Chapters 25–28. It is interesting to compare and contrast the readily visible flows within the atmosphere and oceans to silicate flows occurring within Earth's mantle and in volcanoes; these latter flows are investigated in Chapters 29–35.