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. "...an excellent source of facts for anyone working in functional analysis or operator theory." (Journal of Operator Theory, Vol.53, No.1, 2005) "For years Lax has been counted among the world's very top people in PDEs, so no serious student can afford to ignore his view of the foundations leading up to that subject." (Choice, Vol. 40, No. 4, December 2002) "...attractive...well suited for graduate courses...and useful for research mathematicians." (Mathematical Reviews, 2003a) "...The book is highly recommended to all students of analysis". (Zentralblatt MATH, Vol.1009, No.9, 2003) "A lot of good material, doled out in short chapters." (American Mathematical Monthly, August/September 2003) Peter D. Lax is a Series Advisor for the Wiley Interscience Series in Pure and Applied Mathematics . He is a professor of mathematics at the Courant Institute, the director of the Mathematics and computing Laboratory, and was director of the Institute from 1971 to 1980.