The experimental methods of spectroscopy began, unsurprisingly, in the easily accessible visible regime. Early applications were the observation of the emission spectra of various samples in flame and of the sun. The lines in the visible spectrum of atomic hydrogen were fitted to a formula by Balmer in 1885 and this was the beginning of the close relationship between theory and experiment in spectroscopy, with experiments providing results and the relevant theory attempting to explain them and to predict results in related experiments. The development of Quantum Mechanics in the 1930's coupled with the availability of large, fast computers since the 1960's has allowed predictions of the spectroscopic and structural properties of molecules which are often of comparable accuracy to those obtainable from experiment.
The next section contains an overview of some selected spectroscopies. An outline of photoelectron spectroscopy applied to atoms and molecules is given, in particular for the determination of ionization potentials (or electron removal energies). Additionally, electron loss spectroscopy as applied to the study of collective excitations in solids is introduced. Finally, photoabsorption spectroscopy in small metal clusters is outlined with again particular emphasis on collective electronic excitations (i.e. plasmons).
The spectroscopic methods mentioned are only a small portion of the techniques available (See [1,2] for an introduction). They are, however a representative sample of the spectroscopies available for the investigation of excited states.