  Elliptic N-soliton-type solutions, i.e. solutions emerging from the
application of N consecutive B\"acklund transformations to an elliptic seed
solution, are constructed for all equations in the ABS list of quadrilateral
lattice equations, except for the case of the Q4 equation which is treated
elsewhere. The main construction, which is based on an elliptic Cauchy matrix,
is performed for the equation Q3, and by coalescence on certain auxiliary
parameters, the corresponding solutions of the remaining equations in the list
are obtained. Furthermore, the underlying linear structure of the equations is
exhibited, leading, in particular, to a novel Lax representation of the Q3
equation.
