Introduction.- Slice hyperholomorphic functions.- The S-spectrum and the S-functional calculus.- Properties of the S-functional calculus for bounded operators.- The S-functional calculus for unbounded operators.- The H1 functional calculus.- The F-functional calculus for bounded operators.- The F-functional calculus for unbounded operators.- Quaternionic operators on a Hilbert space.- Spectral integrals.- The spectral theorem for bounded normal operators.-...