This new-in-paperback text is based on lectures given by the author at the advanced undergraduate and graduate levels in Measure Theory, Functional Analysis, Banach Algebras, Spectral Theory (of bounded and unbounded operators), Semigroups of Operators, Probability and Mathematical Statistics, and Partial Differential Equations. The first 10 chapters discuss theoretical methods in Measure Theory and Functional Analysis, and contain over 120 end of chapter exercises. The final two chapters discuss applications in Probability Theory and Partial Differential Equations. Solutions to the end of chapter exercises may be found on the companion website for this text.

Preface; 1. Measures; 2. Construction of measures; 3. Measure and topology; 4. Continuous linear functionals; 5. Duality; 6. Bounded operators; 7. Banach algebras; 8. Hilbert spaces; 9. Integral representation; 10. Unbounded operators; Application I:Probability; Application II: Distributions; Bibliography; Index

Shmuel KantorovitzBar-Ilan Univerity, Israel

`Review from previous edition Here we have the distilled and refined essence of the fruits of world-renowned functional analyst Kantorovitz, who spent 40 years teaching functional analysis to aspiring students of that domain. Everything one might reasonably expect such a student to understand is here, masterfully presented ... A strong bibliography and thorough index nicely complement the main work ... Highly recommended.' F.E.J. Linton, Wesleyan University (Choice)