  In the present work, we consider the existence and spectral stability of
multi-pulse solutions in Hamiltonian lattice systems. We provide a general
framework for the study of such wave patterns based on a discrete analogue of
Lin's method, previously used in the continuum realm. We develop explicit
conditions for the existence of $m$-pulse structures and subsequently develop a
reduced matrix allowing us to address their spectral stability. As a
prototypical example for the manifestation of the details of the formulation,
we consider the discrete nonlinear Schr\"{o}dinger equation. Different families
of $2$- and $3$-pulse solitary waves are discussed, and analytical expressions
for the corresponding stability eigenvalues are obtained which are in very good
agreement with numerical results.
