Foreword 1.Linear Spaces 2.Linear Maps 3.The Hahn-Banach Theorem 4.Applications of the Hahn-Banach theorem 5.Normed Linear Spaces 6.Hilbert Space 7.Applications of Hilbert Space Results 8.Duals of Normed Linear Speaces 9.Applications of Duality 10.Weak Convergence 11.Applications of Weak Convergence 12.The Weak and Weak Topologies 13.Locally Convex Topologies and the Krein-Milman Theorem 14.Examples of Convex Sets and Their Extreme Points 15.Bounded Linear Maps 16.Examples of Bounded Linear Maps 17.Banach Algebras and their Elementary Spectral Theory 18.Gelfand's Theory of Commutative Banach Algebras 19.Applications of Gelfand's Theory of Commutative Banach Algebras 20.Examples of Operators and Their Spectra 21.Compact Maps 22.Examples of Compact Operators 23.Positive compact operators 24.Fredholm's Theory of Integral Equations 25.Invariant Subspaces 26.Harmonic Analysis on a Halfline 27.Index Theory 28.Compact Symmetric Operators in Hilbert Space 29.Examples of Compact Sysmmetric Operators 30.Trace Class and Trace Formula 31.Spectral Theory of Symmetric,Normal,and Unitary Operators 32.Spectral Theory of Self-Adjoint Operators 33.Examples of Self-Adjoint Operators 34.Semigroups of Operators 35.Groups of Unitary Operators 36.Examples of Strongly Continuous Semigroups 37.Scattering Theory 38.A Theorem of Beurling A.Riesz-Kakutani representation theorem B.Theory of distrbutions C.Zorn's Lemma Author Index Subject Index