  We show that every point in a uniformly $2$-nondegenerate CR hypersurface is
canonically associated with a model $2$-nondegenerate structure. The
$2$-nondegenerate models are basic CR invariants playing the same fundamental
role as quadrics do in the Levi nondegenerate case. We characterize all
$2$-nondegenerate models and show that the moduli space of such hypersurfaces
in $\mathbb{C}^N$ is infinite dimensional for each $N>3$. We derive a normal
form for these models' defining equations that is unique up to an action of a
finite dimensional Lie group. We generalize recently introduced CR invariants
termed modified symbols, and show how to compute these intrinsically defined
invariants from a model's defining equation. We show that these models
automatically possess infinitesimal symmetries spanning a complement to their
Levi kernel and derive explicit formulas for them.
