  In 1997, Chekanov gave the first example of a Legendrian nonsimple knot type:
the $m(5_2)$ knot. Epstein, Fuchs, and Meyer extended his result by showing
that there are at least $n$ different Legendrian representatives with maximal
Thurston--Bennequin number of the twist knot $K_{-2n}$ with crossing number
$2n+1$. In this paper we give a complete classification of Legendrian and
transverse representatives of twist knots. In particular, we show that
$K_{-2n}$ has exactly $\lceil\frac{n^2}2\rceil$ Legendrian representatives with
maximal Thurston--Bennequin number, and $\lceil\frac{n}{2}\rceil$ transverse
representatives with maximal self-linking number. Our techniques include convex
surface theory, Legendrian ruling invariants, and Heegaard Floer homology.
