This monograph is devoted to covering the main results in the oscillation and spectral theory of symplectic difference systems. As a pioneer monograph in this field it contains nowadays standard theory of symplectic systems, as well as the most current results in this field, which based on the recently developed comparative index theory. In the last twenty years, various results from the qualitative theory of symplectic and Hamiltonian difference systems were obtained. However, there is no book or a survey paper presenting in a unified way the results of the qualitative theory of symplectic difference systems. This book fills this gap by providing numerous results and citations, which are till now scattered only in journal papers.