Complex symplectic spaces, defined earlier by the authors in their AMS Mono-
graph, are non-trivial generalizations of the real symplectic spaces of classical an-
alytical dynamics. These spaces can also be viewed as non—degenerate indefinite
inner product spaces, although the authors here follow the lesser known exposition
within complex symplectic algebra and geometry, as is appropriate for their prior
development of boundary value theory. In the case of finite dimensional complex
symplectic spaces it was shown that the corresponding symplectic algebra is impor-
tant for the description and classification of all self—adjoint boundary value problems
for (linear) ordinary differential equations on a real interval. In later AMS Memoirs
infinite dimensional complex symplectic spaces were introduced for the analysis of
multi—interval systems and elliptic partial differential operators.