  We discuss strong gravitational lensing by multiple objects along any line of
sight. The probability for strong gravitational lensing by more than one lens
is small, but a number of strong lens systems in which more than one separate
lens contribute significantly to the lensing potential will be detected in the
large sample of lens systems compiled with new instruments. Using multi-lens
ray-tracing, we estimate the likelihood for gravitational lensing by two lenses
at different redshifts and investigate typical image geometries and
magnification cross sections. We find that, for a cosmology with Omega_M=0.3
and Omega_Lambda=0.7, about one in twenty lens systems consist of two lenses
with merging caustics. Multiple lens systems differ from single lenses. They
have a larger multiple imaging cross section and significantly differ in the
image configuration. The external shear induced by a nearby galaxy, group or
cluster can affect image positions even for more widely separated lens pairs.
Both of these effects must be accounted for in lens modelling. We also show how
the presence of aligned discs in the pair of lensing galaxies can lead to very
large high-magnification cross sections. Multiple lens systems will be
important in future, both for constraining lens models of individual systems
and for statistical lensing.
