  Among the 25 planetary systems detected up to now by gravitational
microlensing, there are two cases of a star with two planets, and two cases of
a binary star with a planet. Other, yet undetected types of triple lenses
include triple stars or stars with a planet with a moon. The analysis and
interpretation of such events is hindered by the lack of understanding of
essential characteristics of triple lenses, such as their critical curves and
caustics. We present here analytical and numerical methods for mapping the
critical-curve topology and caustic cusp number in the parameter space of
$n$-point-mass lenses. We apply the methods to the analysis of four symmetric
triple-lens models, and obtain altogether 9 different critical-curve topologies
and 32 caustic structures. While these results include various generic types,
they represent just a subset of all possible triple-lens critical curves and
caustics. Using the analyzed models, we demonstrate interesting features of
triple lenses that do not occur in two-point-mass lenses. We show an example of
a lens that cannot be described by the Chang-Refsdal model in the wide limit.
In the close limit we demonstrate unusual structures of primary and secondary
caustic loops, and explain the conditions for their occurrence. In the
planetary limit we find that the presence of a planet may lead to a whole
sequence of additional caustic metamorphoses. We show that a pair of planets
may change the structure of the primary caustic even when placed far from their
resonant position at the Einstein radius.
