This introductory chapter summarizes concepts of quantum mechanical tunnelling, with their key applications historically and, in particular, their applications to an energy spectroscopy of solids. Superconducting quasiparticle tunnelling (Giaever tunnelling) and Josephson tunnelling are described and illustrated with key examples. Inelastic electron tunnelling spectroscopy (IETS) and the scanning tunnelling microscope (STM), with particular emphasis on its development to produce spectroscopic images in the category of scanning tunnelling spectroscopy (STS). The spatial and energy resolutions of this method are presented. Illustrations of the power of STS include details of the high temperature superconducting state in layered cuprates HTC, and energies and spatial distribution of vibrational motions in single molecules adsorbed to a metal surface.
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