  We study the spectral properties of Schr\"{o}dinger operators on perturbed
lattices. We shall prove the non-existence or the discreteness of embedded
eigenvalues, the limiting absorption principle for the resolvent, construct a
spectral representation, and define the S-matrix. Our theory covers the square,
triangular, diamond, Kagome lattices, as well as the ladder, the graphite and
the subdivision of square lattice.
