  Adler's lattice equation has acquired the status of a master equation among
2D discrete integrable systems. In this paper we derive what we believe are the
first explicit solutions of this equation. In particular it turns out necessary
to establish a non-trivial seed solution from which soliton solutions can
subsequently be constructed using the B\"acklund transformation. As a corollary
we find the corresponding solutions of the Krichever-Novikov equation which is
obtained from Adler's equation in a continuum limit.
