  In recent years there have been new insights into the integrability of
quadrilateral lattice equations, i.e. partial difference equations which are
the natural discrete analogues of integrable partial differential equations in
1+1 dimensions. In the scalar (i.e. single-field) case there now exist
classification results by Adler, Bobenko and Suris (ABS) leading to some new
examples in addition to the lattice equations "of KdV type" that were known
since the late 1970s and early 1980s. In this paper we review the construction
of soliton solutions for the KdV type lattice equations and use those results
to construct N-soliton solutions for all lattice equations in the ABS list
except for the elliptic case of Q4, which is left to a separate treatment.
