This thesis is based on studies of multiple ionization of atoms and molecules induced by the absorption of a single photon. For the experimental investigations a time-of-flight magnetic bottle spectrometer has been used to detect the emitted electrons in coincidence. The method of coincidence time-of-flight spectroscopy and the experimental setup used is described. Experimental and theoretical results on molecular double core holes (DCHs) and multiple ionization of atoms are presented.

Molecular DCHs are of considerable interest, as their chemical shifts are predicted to be more sensitive than their single core hole counterparts. Using CH₄ and NH₃ as examples, it is shown that molecules with two vacancies in the innermost shell can be studied using synchrotron light in combination with our coincidence technique. The chemical shifts of S 2p DCHs are investigated for the molecules CS₂, H₂S and SO₂ and the influence of relaxation effects on the shifts are estimated. In the studies of atoms, the main focus is on the processes leading to double and higher degrees of ionization, and the final state populations. In cadmium double photoionization in the photon energy region 40-200 eV occurs mainly by indirect ionization via valence ionized satellite states and through Coster-Kronig decay of inner shell hole states. In valence-valence ionization of krypton by 88 eV photons both direct and indirect ionization processes are found to be important. For the indirect pathways strong final state selectivity in the autoionization decays of the intermediate states is observed. Triple ionization of krypton via intermediate core-valence doubly ionized states is investigated. The intermediate states are observed in the energy region 120-125 eV, and their decay to states of the triply charged ion is mapped. Experimental and theoretical results on the formation of 2p double hole states in argon are presented.