The flow of viscous fluids traditionally has not received a lot of attention in geology and geophysics curricula. The discussion of mechanics more usually focusses on elasticity and brittle fracture, with which the propagation of seismic (elastic) waves and faulting of the crust and lithosphere may be considered. The formation of folds and other kinds of distributed deformation receives some attention in structural geology, but many geologists still may not be very familiar with the mechanics of fluids. The text by Turcotte and Schubert [1] has gone a considerable way towards filling this gap, but fluid flow is so fundamental to mantle convection that it is worth developing here. By doing this I can focus the development on the particular things needed to treat mantle convection, and I can also present it at a range of mathematical levels, from the simplest possible to some more advanced aspects.

To guide readers, some of the sections are marked Intermediate or Advanced. These labels indicate the mathematical level. The essence of the chapter can be obtained just from the unlabelled sections (6.1, 6.7, 6.8.1, 6.9, 6.10). The important concepts and results are presented in those sections with minimal mathematics. The intermediate sections include mathematical formulations of stress, strain rate, viscosity and the equations governing slow flow of viscous fluids. These should not be too challenging, though some practice may be required if the notation is unfamiliar. A couple of sections summarise more advanced results that have particular relevance here, for those who may wish to see them.

It is always useful to begin with the simplest mathematical treatment that can capture a piece of physics, because then the physical concepts are the least obscured by the mathematics.