  With the advent of high-quality surveys in cosmology the full three-point
correlation function will be a valuable statistic for describing structure
formation models. It contains information on cosmological parameters and
detailed halo properties that cannot be extracted from the two-point
correlation function. We use the halo clustering model to analytically
calculate the three-point correlation function (3PCF) for general cosmological
fields. We present detailed results for the configuration dependence of the
3-dimensional mass and galaxy distributions and the 2-dimensional cosmic shear
field. We work in real space, where higher order correlation functions on small
scales are easier to measure and interpret, but halo model calculations get
rapidly intractable. Hence we develop techniques for accurate evaluations of
the 1, 2 and 3-halo contributions to the 3PCF.
  The 3PCF violates the hierarchical ansatz in both its scale and configuration
dependence. We study the behavior of the coefficient Q in the hierarchical
expansion from large, quasilinear scales down to about 20 kpc. We find that the
nonlinear 3PCF is sensitive to the halo profile of massive halos, especially
its inner slope. We model the distribution of galaxies in halos and show that
the 3PCF of red galaxies has a weaker configuration and scale dependence than
the mass, while for blue galaxies it is very sensitive to the parameters of the
galaxy formation model. The 3PCF from weak lensing on the other hand shows
different scalings due to projection effects and a sensitivity to cosmological
parameters.
