Includes sections on the spectral resolution and spectral representation of self adjoint operators, invariant subspaces, strongly continuous one–parameter semigroups, the index of operators, the trace formula of Lidskii, the Fredholm determinant, and more. ∗ Assumes prior knowledge of Naive set theory, linear algebra, point set topology, basic complex variable, and real variables. ∗ Includes an appendix on the Riesz representation theorem.

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