Hilbert spaces. Spectral theory in finite dimensional spaces. Spectral properties of bounded and compact linear operators. Spectral theorem of bounded normal operators. Spectral representation of bounded self-adjoint operators. Unbounded linear operators and their adjoints. Closed operators. Spectral representation of unitary operators. Spectral representation of unbounded self-adjoint operators. Regular Sturm-Liouville operators. Linear operators in quantum mechanics.