  We develop a Thom-Mather theory of frontals analogous to Ishikawa's theory of
deformations of Legendrian singularities but at the frontal level, avoiding the
use of the contact setting. In particular, we define concepts like frontal
stability, versality of frontal unfoldings or frontal codimension. We prove
several characterizations of stability, including a frontal Mather-Gaffney
criterion, and of versality. We then define the method of reduction with which
we show how to construct frontal versal unfoldings of plane curves and show how
to construct stable unfoldings of corank 1 frontals with isolated instability
which are not necessarily versal. We prove a frontal version of Mond's
conjecture in dimension 1. Finally, we classify stable frontal multigerms and
give a complete classification of corank 1 stable frontals from $\mathbb C^3$
to $\mathbb C^4$.
