This research monograph forms an introduction to the geometry of spaces with an indefinite metric. It then goes on to develop the foundations of the theory of linear operators in these spaces and examines the theory of invariant subspaces, spectral questions and the question of the extension of operators. The subject has applications to a wide variety of fields, including differential equation theory, geometry and theoretical physics. Some of these applications are described in the book. Each section concludes with problems and, in many cases, hints to their solution are also included.

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