  In 1967, Japanese physicist Morikazu Toda published the seminal papers
exhibiting soliton solutions to a chain of particles with nonlinear
interactions between nearest neighbors. In the decades that followed, Toda's
system of particles has been generalized in different directions, each with its
own analytic, geometric, and topological characteristics that sets it apart
from the others. These are known collectively as the Toda lattice. This survey
describes and compares several versions of the finite non-periodic Toda lattice
from the perspective of their geometry and topology.
