This modern introduction to operator theory on spaces with indefinite inner product discusses the geometry and the spectral theory of linear operators on these spaces, the deep interplay with complex analysis, and applications to interpolation problems. The text covers the key results from the last four decades in a readable way with full proofs provided throughout. Step by step, the reader is guided through the intricate geometry and topology of spaces with indefinite inner product, before progressing to a presentation of the geometry and spectral theory on these spaces. The author carefully...