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.