  Dynamical scattering of binaries and triple systems of stars, planets, and
compact objects may produce highly inclined triple systems subject to
Kozai-Lidov (KL) oscillations, potentially leading to collisions, mergers, Type
Ia supernovae, and other phenomena. We present the results of more than 400
million gravitational scattering experiments of binary-binary, triple-single,
and triple-binary scattering. We compute the cross sections for all possible
outcomes and explore their dependencies on incoming velocity, mass, semi-major
axis, and eccentricity, including analytic fits and discussion of the velocity
dependence. For the production of new triple systems by scattering we find that
compact triples are preferred, with ratios of outer to inner semi-major axes of
~few--100, flat or quasi-thermal eccentricity distributions, and flat
distributions in cosine of the mutual inclination. Dynamically formed triples
are thus subject to strong KL oscillations, the "eccentric Kozai mechanism,"
and non-secular effects. For single and binary flyby encounters with triple
systems, we compute the cumulative cross section for changes to the mutual
inclination, eccentricity, and semi-major axis ratio. We apply these results to
scattering events in the field, open clusters, and globular clusters, and
explore the implications for Type Ia supernovae via collisions and mergers,
stellar collisions, and the lifetime and dynamical isolation of triple systems
undergoing KL oscillations. An Appendix provides an analysis of the velocity
dependence of the collision cross section in binary-single scattering.
