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Introduction.- Hilbert Spaces.- Bounded Linear Operators on Hilbert Spaces.- Laurent and Toeplitz Operators on Hilbert Spaces.- Spectral Theory of Compact Self-Adjoint Operators.- Spectral Theory of Integral Operators.- Unbounded Operators on Hilbert Spaces.- Oscillations of an Elastic String.- Operational Calculus with Applications.- Solving Linear Equations by Iterative Methods.- Further Developments of the Spectral Theorem.- Banach Spaces.- Linear Operators Banach Spaces.- Compact Operators on Banach Spaces.- Poincaré Operators: Determinant and Trace.- Fredholm Operators.- Toeplitz and Singular Integral Operators.- Nonlinear Operators.