  Maxwell's investigations into the stability of Saturn's rings provide one of
the earliest analyses of the dynamics of astrophysical discs. Current research
in planetary rings extends Maxwell's kinetic theory to treat dense granular
gases of particles undergoing moderately frequent inelastic collisions. Rather
than disrupting the rings, local instabilities may be responsible for
generating their irregular radial structure. Accretion discs around black holes
or compact stars consist of a plasma permeated by a tangled magnetic field and
may be compared with laboratory fluids through an analogy that connects
Maxwell's researches in electromagnetism and viscoelasticity. A common theme in
this work is the appearance of a complex fluid with a dynamical constitutive
equation relating the stress in the medium to the history of its deformation.
