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Functional analysis, as a book category, covers the mathematical study of infinite-dimensional vector spaces together with the topology and linear operators that act on them; it brings together ideas from linear algebra, real and complex analysis, and topology to treat objects such as normed and metric spaces, Banach and Hilbert spaces, bounded and unbounded operators, spectral theory, distributions, and function spaces (e.g., Sobolev spaces). Books in this category range from introductory texts for advanced undergraduates or beginning graduate students—emphasizing basic theorems, examples and techniques—to highly specialized monographs on operator algebras, semigroups, PDE methods, or applications in quantum mechanics, signal processing and optimization; typical prerequisites are rigorous calculus/real analysis, linear algebra and some point-set topology.

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